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Journal of Applied Mathematics and Computing

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01.06.2015 | Original Research

On the \(\beta \)-Ulam–Hyers–Rassias stability of nonautonomous impulsive evolution equations

verfasst von: Xiulan Yu, JinRong Wang, Yuruo Zhang

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2015

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Abstract

In this paper, we first present \(\beta \)-Ulam–Hyers–Rassias stability results for nonautonomous impulsive evolution equations on a compact interval and an unbounded interval. Second, we give some extensions of \(\beta \)-Ulam–Hyers–Rassias stability for infinite impulses case. Finally, we give two examples to illustrate our results.

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Ahmed, N.U.: Existence of optimal controls for a general class of impulsive systems on Banach space. SIAM J. Control Optimal 42, 669–685 (2003)CrossRefMATH

András, S., Kolumbán, J.J.: On the Ulam–Hyers stability of first order differential systems with nonlocal initial conditions. Nonlinear Anal. TMA 82, 1–11 (2013)CrossRefMATH

Bainov, D.D., Simeonov, P.S.: Integral Inequalities and Applications. Kluwer Academic Publishers, Dordrecht (1992)CrossRefMATH

Balachandran, V.K.: Topological Algebras. Narosa Publishing House, New Delhi (1999)MATH

Benchohra, M., Henderson, J., Ntouyas, S.: Impulsive Differential Equations and Inclusions, Vol. 2 of Contemporary Mathematics and Its Applications. Hindawi, New York (2006)CrossRef

Brzdȩk J., Brillouët-Belluot N., Ciepliński K., Xu B.: Ulam’s type stability. Abst. Appl. Anal. 2012, Article ID 329702, 1–2 (2012)

Burger, M., Ozawa, N., Thom, A.: On Ulam stability. Isr. J. Math. 193, 109–129 (2013)CrossRefMATHMathSciNet

Cădariu, L.: Stabilitatea Ulam–Hyers–Bourgin Pentru Ecuatii Functionale. Ed. Univ. Vest Timişoara, Timişoara (2007)

Chang, Y.K., Li, W.T.: Existence results for second order impulsive functional differential inclusions. J. Math. Anal. Appl. 301, 477–490 (2005)CrossRefMATHMathSciNet

10.

Ciepliński, K.: Stability of multi-additive mappings in \(\beta \)-Banach spaces. Nonlinear Anal.:TMA 75, 4205–4212 (2012)CrossRefMATH

11.

Cimpean, D.S., Popa, D.: Hyers–Ulam stability of Euler’s equation. Appl. Math. Lett. 24, 1539–1543 (2011)CrossRefMATHMathSciNet

12.

Jung, S.M., Kim, T.S., Lee, K.S.: A fixed point approach to the stability of quadratic functional equation. Bull. Korean Math. Soc. 43, 531–541 (2006)CrossRefMATHMathSciNet

13.

Jung, S.M.: Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis. Springer, New York (2011)CrossRefMATH

14.

Jung, S.M., Popa, D., Rassias, MTh: On the stability of the linear functional equation in a single variable on complete metric groups. J. Glob. Optim. 59, 165–171 (2014)CrossRefMATHMathSciNet

15.

Hegyi, B., Jung, S.M.: On the stability of Laplace’s equation. Appl. Math. Lett. 26, 549–552 (2013)CrossRefMATHMathSciNet

16.

Hyers, D.H., Rassias, ThM: Approximate homomorphisms. Aequationes Math. 44, 125–153 (1992)CrossRefMATHMathSciNet

17.

Hyers, D.H., Isac, G., Rassias, ThM: Stability of Functional Equations in Several Variables. Birkhauser, Boston (1998)CrossRefMATH

18.

Liu, J.H.: Nonlinear impulsive evolution equations. Dyn. Contin. Discrete Impuls. Syst. 6, 77–85 (1999)MATH

19.

Lungu, N., Popa, D.: Hyers–Ulam stability of a first order partial differential equation. J. Math. Anal. Appl. 385, 86–91 (2012)CrossRefMATHMathSciNet

20.

Miura, T., Miyajima, S., Takahasi, S.E.: A characterization of Hyers–Ulam stability of first order linear differential operators. J. Math. Anal. Appl. 286, 136–146 (2003)CrossRefMATHMathSciNet

21.

Obłoza, M.: Connections between Hyers and Lyapunov stability of the ordinary differential equations. Rocznik Nauk. Dydakt. Prace Mat. 14, 141–146 (1997)MATH

22.

Otrocol, D., Llea, V.: Ulam stability for a delay differential equation. Cent. Eur. J. Math. 11, 1296–1303 (2013)CrossRefMATHMathSciNet

23.

Pazy, A.: Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)CrossRef

24.

Rassias, J.M.: On the stability of functional equations in Banach spaces. J. Math. Anal. Appl. 251, 264–284 (2000)CrossRefMATHMathSciNet

25.

Rassias, J.M.: On the stability of functional equations and a problem of Ulam. Acta Appl. Math. 62, 23–130 (2000)CrossRefMATHMathSciNet

26.

Rassias, Th.M., Brzdek, J.: Functional Equations in Mathematical Analysis. Springer, New York (2012)

27.

Rezaei, H., Jung, S.M., Rassias, Th.M.: Laplace transform and Hyers-Ulam stability of linear differential equations. J. Math. Anal. Appl. 403, 244–251 (2013)

28.

Rus, I.A.: Ulam stabilities of ordinary differential equations in a Banach space. Carpathian J. Math. 26, 103–107 (2010)MATHMathSciNet

29.

Takahasi, S.E., Miura, T., Miyajima, S.: On the Hyers–Ulam stability of the Banach space-valued differential equation \(y^{\prime } = \lambda y\). Bull. Korean Math. Soc. 39, 309–315 (2002)CrossRefMATHMathSciNet

30.

Wang, J., Fečkan, M., Zhou, Y.: Ulam’s type stability of impulsive ordinary differential equations. J. Math. Anal. Appl. 395, 258–264 (2012)CrossRefMATHMathSciNet

31.

Wang J., Xiang X., Wei W., Chen Q.: Existence and global asymptotical stability of periodic solution for the \(T\)-periodic Logistic system with time-varying generating operators and \(T_{0}\)-periodic impulsive perturbations on Banach spaces. Discrete Dyn. Nat. Soc. 2008, Art. ID 524945, 1–16 (2008)

32.

Wei, W., Hou, S.H., Teo, K.L.: On a class of strongly nonlinear impulsive differential equation with time delay. Nonlinear Dyn. Syst. Theory 6, 281–293 (2006)MATHMathSciNet

33.

Xu, T.Z.: On the stability of multi-Jensen mappings in \(\beta \)-normed spaces. Appl. Math. Lett. 25, 1866–1870 (2012)CrossRefMATHMathSciNet

Titel: On the -Ulam–Hyers–Rassias stability of nonautonomous impulsive evolution equations
verfasst von: Xiulan Yu
JinRong Wang
Yuruo Zhang
Publikationsdatum: 01.06.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2015
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-014-0813-2

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