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2017 | OriginalPaper | Buchkapitel

11. On the Qualitative Behaviors of Nonlinear Functional Differential Systems of Third Order

verfasst von : Cemil Tunç

Erschienen in: Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

Verlag: Springer Singapore

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Abstract

In this paper, the author gives new sufficient conditions for the boundedness and globally asymptotically stability of solutions to certain nonlinear delay functional differential systems of third order. The technique of proof involves defining an appropriate Lyapunov–Krasovskii functional and applying LaSalle’s invariance principle. The obtained results include and improve the results in literature.

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Literatur
1.
Zurück zum Zitat Adams, D.O., Omeike, M.O., Mewomo, O.T., Olusola, I.O.: Boundedness of solutions of some third order non-autonomous ordinary differential equations. J. Niger. Math. Soc. 32, 229–240 (2013)MathSciNetMATH Adams, D.O., Omeike, M.O., Mewomo, O.T., Olusola, I.O.: Boundedness of solutions of some third order non-autonomous ordinary differential equations. J. Niger. Math. Soc. 32, 229–240 (2013)MathSciNetMATH
2.
Zurück zum Zitat Ademola, T.A., Arawomo, P.O.: Stability and ultimate boundedness of solutions to certain third-order differential equations. Appl. Math. E-Notes 10, 61–69 (2010)MathSciNetMATH Ademola, T.A., Arawomo, P.O.: Stability and ultimate boundedness of solutions to certain third-order differential equations. Appl. Math. E-Notes 10, 61–69 (2010)MathSciNetMATH
3.
Zurück zum Zitat Ademola, T.A., Arawomo, P.O.: Stability and uniform ultimate boundedness of solutions of some third-order differential equations. Acta Math. Acad. Paedagog. Nyházi. (N.S.) 27, 51–59 (2011) Ademola, T.A., Arawomo, P.O.: Stability and uniform ultimate boundedness of solutions of some third-order differential equations. Acta Math. Acad. Paedagog. Nyházi. (N.S.) 27, 51–59 (2011)
4.
Zurück zum Zitat Ademola, T.A., Arawomo, P.O.: Asymptotic behaviour of solutions of third order nonlinear differential equations. Acta Univ. Sapientiae Math. 3, 197–211 (2011)MathSciNetMATH Ademola, T.A., Arawomo, P.O.: Asymptotic behaviour of solutions of third order nonlinear differential equations. Acta Univ. Sapientiae Math. 3, 197–211 (2011)MathSciNetMATH
5.
Zurück zum Zitat Ademola, T.A., Arawomo, P.O.: Uniform stability and boundedness of solutions of nonlinear delay differential equations of the third order. Math. J. Okayama Univ. 55, 157–166 (2013)MathSciNetMATH Ademola, T.A., Arawomo, P.O.: Uniform stability and boundedness of solutions of nonlinear delay differential equations of the third order. Math. J. Okayama Univ. 55, 157–166 (2013)MathSciNetMATH
6.
Zurück zum Zitat Ademola, A.T., Ogundare, B.S., Ogundiran, M.O., Adesina, O.A.: Stability, boundedness, and existence of periodic solutions to certain third-order delay differential equations with multiple deviating arguments. Int. J. Differ. Equ. 2015, Art. ID 213935, 12 pp (2015) Ademola, A.T., Ogundare, B.S., Ogundiran, M.O., Adesina, O.A.: Stability, boundedness, and existence of periodic solutions to certain third-order delay differential equations with multiple deviating arguments. Int. J. Differ. Equ. 2015, Art. ID 213935, 12 pp (2015)
7.
Zurück zum Zitat Afuwape, A.U., Castellanos, J.E.: Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: frequency domain method. Appl. Math. Comput. 216, 940–950 (2010)MathSciNetMATH Afuwape, A.U., Castellanos, J.E.: Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: frequency domain method. Appl. Math. Comput. 216, 940–950 (2010)MathSciNetMATH
8.
Zurück zum Zitat Afuwape, A.U., Omari, P., Zanolin, F.: Nonlinear perturbations of differential operators with nontrivial kernel and applications to third-order periodic boundary value problems. J. Math. Anal. Appl. 143, 35–56 (1989)MathSciNetCrossRefMATH Afuwape, A.U., Omari, P., Zanolin, F.: Nonlinear perturbations of differential operators with nontrivial kernel and applications to third-order periodic boundary value problems. J. Math. Anal. Appl. 143, 35–56 (1989)MathSciNetCrossRefMATH
9.
Zurück zum Zitat Afuwape, A.U., Omeike, M.O.: Stability and boundedness of solutions of a kind of third-order delay differential equations. Comput. Appl. Math. 29, 329–342 (2010)MathSciNetCrossRefMATH Afuwape, A.U., Omeike, M.O.: Stability and boundedness of solutions of a kind of third-order delay differential equations. Comput. Appl. Math. 29, 329–342 (2010)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Ahmad, S., Rao, M.R.M.: Theory of ordinary differential equations. With applications in biology and engineering. Affiliated East-West Press Pvt. Ltd., New Delhi (1999) Ahmad, S., Rao, M.R.M.: Theory of ordinary differential equations. With applications in biology and engineering. Affiliated East-West Press Pvt. Ltd., New Delhi (1999)
11.
Zurück zum Zitat Andres, J.: Periodic boundary value problem for certain nonlinear differential equations of the third order. Math. Slovaca 35, 305–309 (1985)MathSciNetMATH Andres, J.: Periodic boundary value problem for certain nonlinear differential equations of the third order. Math. Slovaca 35, 305–309 (1985)MathSciNetMATH
12.
Zurück zum Zitat Animalu, A.O.E., Ezeilo, J.O.C.: Some third order differential equations in physics. Fundamental open problems in science at the end of the millennium, Vol. I–III (Beijing, 1997), pp. 575–586. Hadronic Press, Palm Harbor, FL (1997) Animalu, A.O.E., Ezeilo, J.O.C.: Some third order differential equations in physics. Fundamental open problems in science at the end of the millennium, Vol. I–III (Beijing, 1997), pp. 575–586. Hadronic Press, Palm Harbor, FL (1997)
13.
Zurück zum Zitat Bai, Y., Guo, C.: New results on stability and boundedness of third order nonlinear delay differential equations. Dynam. Systems Appl. 22, 95–104 (2013)MathSciNetMATH Bai, Y., Guo, C.: New results on stability and boundedness of third order nonlinear delay differential equations. Dynam. Systems Appl. 22, 95–104 (2013)MathSciNetMATH
16.
Zurück zum Zitat Eichhorn, R., Linz, S.J., Hänggi, P.: Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows. Phys. Rev. E 58, 7151–7164 (1998)MathSciNetCrossRef Eichhorn, R., Linz, S.J., Hänggi, P.: Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows. Phys. Rev. E 58, 7151–7164 (1998)MathSciNetCrossRef
17.
Zurück zum Zitat Ezeilo, J.O.C., Onyia, J.: Nonresonant oscillations for some third-order differential equations. J. Niger. Math. Soc. 3(1984), 83–96 (1986)MathSciNetMATH Ezeilo, J.O.C., Onyia, J.: Nonresonant oscillations for some third-order differential equations. J. Niger. Math. Soc. 3(1984), 83–96 (1986)MathSciNetMATH
18.
Zurück zum Zitat Ezeilo, J.O.C., Tejumola, H.O.: Further results for a system of third order differential equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58, 143–151 (1975) Ezeilo, J.O.C., Tejumola, H.O.: Further results for a system of third order differential equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58, 143–151 (1975)
19.
Zurück zum Zitat Fridedrichs, K.O.: On nonlinear vibrations of third order. Studies in Nonlinear Vibration Theory, pp. 65–103. Institute for Mathematics and Mechanics, New York University (1946) Fridedrichs, K.O.: On nonlinear vibrations of third order. Studies in Nonlinear Vibration Theory, pp. 65–103. Institute for Mathematics and Mechanics, New York University (1946)
20.
Zurück zum Zitat Graef, J.R., Beldjerd, D., Remili, M.: On stability, ultimate boundedness, and existence of periodic solutions of certain third order differential equations with delay. PanAmer. Math. J. 25, 82–94 (2015)MathSciNetMATH Graef, J.R., Beldjerd, D., Remili, M.: On stability, ultimate boundedness, and existence of periodic solutions of certain third order differential equations with delay. PanAmer. Math. J. 25, 82–94 (2015)MathSciNetMATH
21.
Zurück zum Zitat Graef, J.R., Oudjedi, L.D., Remili, M.: Stability and square integrability of solutions of nonlinear third order differential equations. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 22, 313–324 (2015) Graef, J.R., Oudjedi, L.D., Remili, M.: Stability and square integrability of solutions of nonlinear third order differential equations. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 22, 313–324 (2015)
22.
Zurück zum Zitat Graef, J.R., Tunç, C.: Global asymptotic stability and boundedness of certain multi\(-\)delay functional differential equations of third order. Math. Methods Appl. Sci. 38, 3747–3752 (2015)MathSciNetCrossRefMATH Graef, J.R., Tunç, C.: Global asymptotic stability and boundedness of certain multi\(-\)delay functional differential equations of third order. Math. Methods Appl. Sci. 38, 3747–3752 (2015)MathSciNetCrossRefMATH
23.
Zurück zum Zitat Hale, J.: Sufficient conditions for stability and instability of autonomous functional-differential equations. J. Differential Equations 1, 452–482 (1965)MathSciNetCrossRefMATH Hale, J.: Sufficient conditions for stability and instability of autonomous functional-differential equations. J. Differential Equations 1, 452–482 (1965)MathSciNetCrossRefMATH
24.
Zurück zum Zitat Korkmaz, E., Tunç, C.: Convergence to non-autonomous differential equations of second order. J. Egypt. Math. Soc. 23, 27–30 (2015)MathSciNetCrossRefMATH Korkmaz, E., Tunç, C.: Convergence to non-autonomous differential equations of second order. J. Egypt. Math. Soc. 23, 27–30 (2015)MathSciNetCrossRefMATH
26.
Zurück zum Zitat Mahmoud, A.M., Tunç, C.: Stability and boundedness of solutions of a certain n-dimensional nonlinear delay differential system of third-order. Adv. Pure Appl. Math. 7, 1–11 (2016)MathSciNetMATH Mahmoud, A.M., Tunç, C.: Stability and boundedness of solutions of a certain n-dimensional nonlinear delay differential system of third-order. Adv. Pure Appl. Math. 7, 1–11 (2016)MathSciNetMATH
27.
Zurück zum Zitat Ogundare, B.S.: On boundedness and stability of solutions of certain third order delay differential equation. J. Niger. Math. Soc. 31, 55–68 (2012)MathSciNetMATH Ogundare, B.S.: On boundedness and stability of solutions of certain third order delay differential equation. J. Niger. Math. Soc. 31, 55–68 (2012)MathSciNetMATH
28.
Zurück zum Zitat Ogundare, B.S., Ayanjinmi, J.A., Adesina, O.A.: Bounded and L 2 -solutions of certain third order non-linear differential equation with a square integrable forcing term. Kragujevac J. Math. 29, 151–156 (2006)MathSciNetMATH Ogundare, B.S., Ayanjinmi, J.A., Adesina, O.A.: Bounded and L 2 -solutions of certain third order non-linear differential equation with a square integrable forcing term. Kragujevac J. Math. 29, 151–156 (2006)MathSciNetMATH
29.
Zurück zum Zitat Olutimo, A.L.: Stability and ultimate boundedness of solutions of a certain third order nonlinear vector differential equation. J. Niger. Math. Soc. 31, 69–80 (2012)MathSciNetMATH Olutimo, A.L.: Stability and ultimate boundedness of solutions of a certain third order nonlinear vector differential equation. J. Niger. Math. Soc. 31, 69–80 (2012)MathSciNetMATH
30.
Zurück zum Zitat Omeike, M.O.: Stability and boundedness of solutions of a certain system of third order nonlinear delay differential equations. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 54, 109–119 (2015) Omeike, M.O.: Stability and boundedness of solutions of a certain system of third order nonlinear delay differential equations. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 54, 109–119 (2015)
31.
Zurück zum Zitat Qian, C.: On global stability of third-order nonlinear differential equations. Nonlinear Anal. Ser. A: Theory Methods 42, 651–661 (2000)MathSciNetCrossRefMATH Qian, C.: On global stability of third-order nonlinear differential equations. Nonlinear Anal. Ser. A: Theory Methods 42, 651–661 (2000)MathSciNetCrossRefMATH
32.
Zurück zum Zitat Rauch, L.L.: Oscillation of a third order nonlinear autonomous system. Contributions to the Theory of Nonlinear Oscillations, pp. 39–88. Annals of Mathematics Studies, no. 20. Princeton University Press, Princeton, NJ (1950) Rauch, L.L.: Oscillation of a third order nonlinear autonomous system. Contributions to the Theory of Nonlinear Oscillations, pp. 39–88. Annals of Mathematics Studies, no. 20. Princeton University Press, Princeton, NJ (1950)
33.
Zurück zum Zitat Reissig, R., Sansone, G., Conti, R.: Non-linear differential equations of higher order. Translated from the German. Noordhoff International Publishing, Leyden (1974)MATH Reissig, R., Sansone, G., Conti, R.: Non-linear differential equations of higher order. Translated from the German. Noordhoff International Publishing, Leyden (1974)MATH
34.
Zurück zum Zitat Remili, M., Oudjedi, L.D.:Stability and boundedness of the solutions of non-autonomous third order differential equations with delay. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 53, 139–147 (2014) Remili, M., Oudjedi, L.D.:Stability and boundedness of the solutions of non-autonomous third order differential equations with delay. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 53, 139–147 (2014)
35.
Zurück zum Zitat Sadek, A.I.: Stability and boundedness of a kind of third-order delay differential system. Appl. Math. Lett. 16, 657–662 (2003)MathSciNetCrossRefMATH Sadek, A.I.: Stability and boundedness of a kind of third-order delay differential system. Appl. Math. Lett. 16, 657–662 (2003)MathSciNetCrossRefMATH
36.
Zurück zum Zitat Smith, H.: An introduction to delay differential equations with applications to the life sciences. Texts in Applied Mathematics, 57. Springer, New York (2011) Smith, H.: An introduction to delay differential equations with applications to the life sciences. Texts in Applied Mathematics, 57. Springer, New York (2011)
37.
Zurück zum Zitat Swick, K.E.: Asymptotic behavior of the solutions of certain third order differential equations. SIAM J. Appl. Math. 19, 96–102 (1970)MathSciNetCrossRefMATH Swick, K.E.: Asymptotic behavior of the solutions of certain third order differential equations. SIAM J. Appl. Math. 19, 96–102 (1970)MathSciNetCrossRefMATH
38.
Zurück zum Zitat Tejumola, H.O., Tchegnani, B.: Stability, boundedness and existence of periodic solutions of some third and fourth order nonlinear delay differential equations. J. Niger. Math. Soc. 19, 9–19 (2000)MathSciNet Tejumola, H.O., Tchegnani, B.: Stability, boundedness and existence of periodic solutions of some third and fourth order nonlinear delay differential equations. J. Niger. Math. Soc. 19, 9–19 (2000)MathSciNet
39.
Zurück zum Zitat Tunç, C.: On the boundedness and periodicity of the solutions of a certain vector differential equation of third-order. Chinese translation in Appl. Math. Mech. 20, 153–160 (1999). Appl. Math. Mech. (English Ed.) 20, 163–170 (1999) Tunç, C.: On the boundedness and periodicity of the solutions of a certain vector differential equation of third-order. Chinese translation in Appl. Math. Mech. 20, 153–160 (1999). Appl. Math. Mech. (English Ed.) 20, 163–170 (1999)
40.
Zurück zum Zitat Tunç, C.: Uniform ultimate boundedness of the solutions of third-order nonlinear differential equations. Kuwait J. Sci. Engrg. 32, 39–48 (2005)MathSciNetMATH Tunç, C.: Uniform ultimate boundedness of the solutions of third-order nonlinear differential equations. Kuwait J. Sci. Engrg. 32, 39–48 (2005)MathSciNetMATH
41.
Zurück zum Zitat Tunç, C.: Boundedness of solutions of a third-order nonlinear differential equation. JIPAM. J. Inequal. Pure Appl. Math. 6, Article 3, 1–6 (2005) Tunç, C.: Boundedness of solutions of a third-order nonlinear differential equation. JIPAM. J. Inequal. Pure Appl. Math. 6, Article 3, 1–6 (2005)
42.
Zurück zum Zitat Tunç, C.: On the asymptotic behavior of solutions of certain third-order nonlinear differential equations. J. Appl. Math. Stoch. Anal. 2005, 29–35 (2005)MathSciNetCrossRefMATH Tunç, C.: On the asymptotic behavior of solutions of certain third-order nonlinear differential equations. J. Appl. Math. Stoch. Anal. 2005, 29–35 (2005)MathSciNetCrossRefMATH
43.
Zurück zum Zitat Tunç, C.: New results about stability and boundedness of solutions of certain non-linear third-order delay differential equations. Arab. J. Sci. Eng. Sect. A Sci. 31, 185–196 (2006) Tunç, C.: New results about stability and boundedness of solutions of certain non-linear third-order delay differential equations. Arab. J. Sci. Eng. Sect. A Sci. 31, 185–196 (2006)
44.
Zurück zum Zitat Tunç,C.: On the boundedness of solutions of certain nonlinear vector differential equations of third order. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 49(97), 291–300 (2006) Tunç,C.: On the boundedness of solutions of certain nonlinear vector differential equations of third order. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 49(97), 291–300 (2006)
45.
Zurück zum Zitat Tunç, C.: On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument. Nonlinear Dynam. 57, 97–106 (2009)MathSciNetCrossRefMATH Tunç, C.: On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument. Nonlinear Dynam. 57, 97–106 (2009)MathSciNetCrossRefMATH
46.
Zurück zum Zitat Tunç, C.: On the stability and boundedness of solutions of nonlinear vector differential equations of third order. Nonlinear Anal. 70, 2232–2236 (2009)MathSciNetCrossRefMATH Tunç, C.: On the stability and boundedness of solutions of nonlinear vector differential equations of third order. Nonlinear Anal. 70, 2232–2236 (2009)MathSciNetCrossRefMATH
47.
Zurück zum Zitat Tunç, C.: Bounded solutions to nonlinear delay differential equations of third order. Topol. Methods Nonlinear Anal. 34, 131–139 (2009)MathSciNetCrossRefMATH Tunç, C.: Bounded solutions to nonlinear delay differential equations of third order. Topol. Methods Nonlinear Anal. 34, 131–139 (2009)MathSciNetCrossRefMATH
48.
Zurück zum Zitat Tunç, C.: On the stability and boundedness of solutions of nonlinear third order differential equations with delay. Filomat 24, 1–10 (2010)MathSciNetCrossRefMATH Tunç, C.: On the stability and boundedness of solutions of nonlinear third order differential equations with delay. Filomat 24, 1–10 (2010)MathSciNetCrossRefMATH
49.
Zurück zum Zitat Tunç, C.: Stability and bounded of solutions to non-autonomous delay differential equations of third order. Nonlinear Dynam. 62, 945–953 (2010)MathSciNetCrossRefMATH Tunç, C.: Stability and bounded of solutions to non-autonomous delay differential equations of third order. Nonlinear Dynam. 62, 945–953 (2010)MathSciNetCrossRefMATH
50.
Zurück zum Zitat Tunç, C.: On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations. Electron. J. Qual. Theory Differ. Equ. 2010, 1–19 (2010)MathSciNetMATH Tunç, C.: On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations. Electron. J. Qual. Theory Differ. Equ. 2010, 1–19 (2010)MathSciNetMATH
51.
Zurück zum Zitat Tunç, C.: Stability and boundedness for a kind of non-autonomous differential equations with constant delay. Appl. Math. Inf. Sci. 7, 355–361 (2013)MathSciNetCrossRef Tunç, C.: Stability and boundedness for a kind of non-autonomous differential equations with constant delay. Appl. Math. Inf. Sci. 7, 355–361 (2013)MathSciNetCrossRef
52.
Zurück zum Zitat Tunç, C.: Stability and boundedness of the nonlinear differential equations of third order with multiple deviating arguments. Afr. Mat. 24, 381–390 (2013)MathSciNetCrossRefMATH Tunç, C.: Stability and boundedness of the nonlinear differential equations of third order with multiple deviating arguments. Afr. Mat. 24, 381–390 (2013)MathSciNetCrossRefMATH
53.
Zurück zum Zitat Tunç, C.: On the qualitative behaviors of solutions of some differential equations of higher order with multiple deviating arguments. J. Franklin Inst. 351, 643–655 (2014)MathSciNetCrossRefMATH Tunç, C.: On the qualitative behaviors of solutions of some differential equations of higher order with multiple deviating arguments. J. Franklin Inst. 351, 643–655 (2014)MathSciNetCrossRefMATH
54.
Zurück zum Zitat Tunç, C.: On the stability and boundedness of certain third order non-autonomous differential equations of retarded type. Proyecciones 34, 147–159 (2015)MathSciNetCrossRefMATH Tunç, C.: On the stability and boundedness of certain third order non-autonomous differential equations of retarded type. Proyecciones 34, 147–159 (2015)MathSciNetCrossRefMATH
55.
Zurück zum Zitat Tunç, C.: Global stability and boundedness of solutions to differential equations of third order with multiple delays. Dynam. Syst. Appl. 24, 467–478 (2015)MathSciNetMATH Tunç, C.: Global stability and boundedness of solutions to differential equations of third order with multiple delays. Dynam. Syst. Appl. 24, 467–478 (2015)MathSciNetMATH
56.
Zurück zum Zitat Tunç, C.: Stability and boundedness in delay system of differential equations of third order. J. Assoc. Arab Univ. Basic Appl. Sci., (2016), (in press) Tunç, C.: Stability and boundedness in delay system of differential equations of third order. J. Assoc. Arab Univ. Basic Appl. Sci., (2016), (in press)
57.
Zurück zum Zitat Tunç, C.: Boundedness of solutions to certain system of differential equations with multiple delays. Mathematical Modeling and Applications in Nonlinear Dynamics. Springer Book Series, Chapter 5, 109–123 (2016) Tunç, C.: Boundedness of solutions to certain system of differential equations with multiple delays. Mathematical Modeling and Applications in Nonlinear Dynamics. Springer Book Series, Chapter 5, 109–123 (2016)
58.
Zurück zum Zitat Tunç, C., Ateş, M.: Stability and boundedness results for solutions of certain third order nonlinear vector differential equations. Nonlinear Dynam. 45, 273–281 (2006)MathSciNetCrossRefMATH Tunç, C., Ateş, M.: Stability and boundedness results for solutions of certain third order nonlinear vector differential equations. Nonlinear Dynam. 45, 273–281 (2006)MathSciNetCrossRefMATH
59.
Zurück zum Zitat Tunç, C., Gözen, M.: Stability and uniform boundedness in multidelay functional differential equations of third order. Abstr. Appl. Anal. 2013, Art. ID 248717, 1–7 (2013) Tunç, C., Gözen, M.: Stability and uniform boundedness in multidelay functional differential equations of third order. Abstr. Appl. Anal. 2013, Art. ID 248717, 1–7 (2013)
60.
Zurück zum Zitat Tunç, C., Mohammed, S.A.: On the qualitative properties of differential equations of third order with retarded argument. Proyecciones 33, 325–347 (2014)MathSciNetCrossRefMATH Tunç, C., Mohammed, S.A.: On the qualitative properties of differential equations of third order with retarded argument. Proyecciones 33, 325–347 (2014)MathSciNetCrossRefMATH
61.
Zurück zum Zitat Tunç, C., Tunç, E.: New ultimate boundedness and periodicity results for certain third-order nonlinear vector differential equations. Math. J. Okayama Univ. 48, 159–172 (2006)MathSciNetMATH Tunç, C., Tunç, E.: New ultimate boundedness and periodicity results for certain third-order nonlinear vector differential equations. Math. J. Okayama Univ. 48, 159–172 (2006)MathSciNetMATH
62.
Zurück zum Zitat Tunç, E.: On the convergence of solutions of certain third-order differential equations. Discrete Dyn. Nat. Soc. 2009, Article ID 863178, 1–12 (2009) Tunç, E.: On the convergence of solutions of certain third-order differential equations. Discrete Dyn. Nat. Soc. 2009, Article ID 863178, 1–12 (2009)
63.
Zurück zum Zitat Tunç, E.: Instability of solutions of certain nonlinear vector differential equations of third order. Electron. J. Differ. Eq. 2005, 1–6 (2005)MathSciNetMATH Tunç, E.: Instability of solutions of certain nonlinear vector differential equations of third order. Electron. J. Differ. Eq. 2005, 1–6 (2005)MathSciNetMATH
64.
Zurück zum Zitat Yoshizawa, T.: Stability theory by Liapunov’s second method. Publications of the Mathematical Society of Japan, No. 9. The Mathematical Society of Japan, Tokyo, (1966) Yoshizawa, T.: Stability theory by Liapunov’s second method. Publications of the Mathematical Society of Japan, No. 9. The Mathematical Society of Japan, Tokyo, (1966)
65.
Zurück zum Zitat Zhang, L., Yu, L.: Global asymptotic stability of certain third-order nonlinear differential equations. Math. Methods Appl. Sci. Math. Methods Appl. Sci. 36, 1845–1850 (2013)MathSciNetCrossRefMATH Zhang, L., Yu, L.: Global asymptotic stability of certain third-order nonlinear differential equations. Math. Methods Appl. Sci. Math. Methods Appl. Sci. 36, 1845–1850 (2013)MathSciNetCrossRefMATH
66.
Zurück zum Zitat Zhu, Y.F.: On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system. Ann. Differ. Equ. 8, 249–259 (1992)MathSciNetMATH Zhu, Y.F.: On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system. Ann. Differ. Equ. 8, 249–259 (1992)MathSciNetMATH
Metadaten
Titel
On the Qualitative Behaviors of Nonlinear Functional Differential Systems of Third Order
verfasst von
Cemil Tunç
Copyright-Jahr
2017
Verlag
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-3722-1_11