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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2014

01.10.2014 | Original Research

Existence and uniqueness of periodic solution for prescribed mean curvature Rayleigh type p-Laplacian equation

verfasst von: Dongshu Wang

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2014

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Abstract

In this paper, a prescribed mean curvature Rayleigh type p-Laplacian equation with a deviating argument was investigated. Based on the coincidence degree theory and some analysis techniques, a series of existence and uniqueness results of periodic solution to the equation were obtained. At last, several illustrative examples were given to illustrate the main results.

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Literatur
1.
Zurück zum Zitat Bonheure, D., Habets, P., Obersnel, F., Omari, P.: Classical and non-classical solutions of a prescribed curvature equation. J. Differ. Equ. 243, 208–237 (2007) CrossRefMATHMathSciNet Bonheure, D., Habets, P., Obersnel, F., Omari, P.: Classical and non-classical solutions of a prescribed curvature equation. J. Differ. Equ. 243, 208–237 (2007) CrossRefMATHMathSciNet
2.
Zurück zum Zitat López, R.: A comparisonal result for radial solutions of the mean curvature equation. Appl. Math. Lett. 22, 860–864 (2009) CrossRefMATHMathSciNet López, R.: A comparisonal result for radial solutions of the mean curvature equation. Appl. Math. Lett. 22, 860–864 (2009) CrossRefMATHMathSciNet
3.
Zurück zum Zitat Pan, H.: One-dimensional prescribed mean curvature equation with exponential nonlinearity. Nonlinear Anal. 70, 999–1010 (2009) CrossRefMATHMathSciNet Pan, H.: One-dimensional prescribed mean curvature equation with exponential nonlinearity. Nonlinear Anal. 70, 999–1010 (2009) CrossRefMATHMathSciNet
4.
Zurück zum Zitat Obersnel, F., Omari, P.: Positive solutions of the Dirichlet problem for the prescribed mean curvature equation. J. Differ. Equ. 249, 1674–1725 (2010) CrossRefMATHMathSciNet Obersnel, F., Omari, P.: Positive solutions of the Dirichlet problem for the prescribed mean curvature equation. J. Differ. Equ. 249, 1674–1725 (2010) CrossRefMATHMathSciNet
5.
Zurück zum Zitat Benevieria, P., Do Ó, J.M., Medeiros, E.S.: Periodic solutions for nonlinear systems with mean curvature-like operators. Nonlinear Anal. 65, 1462–1475 (2006) CrossRefMathSciNet Benevieria, P., Do Ó, J.M., Medeiros, E.S.: Periodic solutions for nonlinear systems with mean curvature-like operators. Nonlinear Anal. 65, 1462–1475 (2006) CrossRefMathSciNet
6.
Zurück zum Zitat Li, W., Liu, Z.: Exact number of solutions of a prescribed mean curvature equation. J. Math. Anal. Appl. 367, 486–498 (2010) CrossRefMATHMathSciNet Li, W., Liu, Z.: Exact number of solutions of a prescribed mean curvature equation. J. Math. Anal. Appl. 367, 486–498 (2010) CrossRefMATHMathSciNet
7.
8.
Zurück zum Zitat Pan, H., Xing, R.: Exact multiplicity results for a one-dimensional prescribed mean curvature problem related to MEMS models. Nonlinear Anal., Real World Appl. 13, 2432–2445 (2012) CrossRefMATHMathSciNet Pan, H., Xing, R.: Exact multiplicity results for a one-dimensional prescribed mean curvature problem related to MEMS models. Nonlinear Anal., Real World Appl. 13, 2432–2445 (2012) CrossRefMATHMathSciNet
9.
Zurück zum Zitat Feng, M.: Periodic solutions for prescribed mean curvature Liénard equation with a deviating argument. Nonlinear Anal., Real World Appl. 13, 1216–1223 (2012) CrossRefMATHMathSciNet Feng, M.: Periodic solutions for prescribed mean curvature Liénard equation with a deviating argument. Nonlinear Anal., Real World Appl. 13, 1216–1223 (2012) CrossRefMATHMathSciNet
11.
Zurück zum Zitat Pino, M., Guerra, I.: Ground states of a prescribed mean curvature equation. J. Differ. Equ. 241, 112–129 (2007) CrossRefMATH Pino, M., Guerra, I.: Ground states of a prescribed mean curvature equation. J. Differ. Equ. 241, 112–129 (2007) CrossRefMATH
12.
Zurück zum Zitat Pan, H., Xing, R.: Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations II. Nonlinear Anal., Theory Methods Appl. 74, 3751–3768 (2011) CrossRefMATHMathSciNet Pan, H., Xing, R.: Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations II. Nonlinear Anal., Theory Methods Appl. 74, 3751–3768 (2011) CrossRefMATHMathSciNet
14.
Zurück zum Zitat Wang, L., Shao, J.: New results of periodic solutions for a kind of forced Rayleigh-type equations. Nonlinear Anal., Real World Appl. 11, 99–105 (2010) CrossRefMATHMathSciNet Wang, L., Shao, J.: New results of periodic solutions for a kind of forced Rayleigh-type equations. Nonlinear Anal., Real World Appl. 11, 99–105 (2010) CrossRefMATHMathSciNet
15.
Zurück zum Zitat Li, Y., Huang, L.: New results of periodic solutions for forced Rayleigh-type equations. J. Comput. Appl. Math. 231(1), 99–105 (2008) Li, Y., Huang, L.: New results of periodic solutions for forced Rayleigh-type equations. J. Comput. Appl. Math. 231(1), 99–105 (2008)
16.
Zurück zum Zitat Lu, S., Ge, W.: Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear Anal. 56, 501–514 (2005) CrossRefMathSciNet Lu, S., Ge, W.: Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear Anal. 56, 501–514 (2005) CrossRefMathSciNet
17.
Zurück zum Zitat Wang, G., Cheng, S.: A priori bounds for periodic solutions of a delay Rayleigh equation. Appl. Math. Lett. 12, 41–44 (1999) CrossRefMATHMathSciNet Wang, G., Cheng, S.: A priori bounds for periodic solutions of a delay Rayleigh equation. Appl. Math. Lett. 12, 41–44 (1999) CrossRefMATHMathSciNet
19.
Zurück zum Zitat Zong, M., Liang, H.: Periodic solutions for Rayleigh type p-Laplacian equation with deviating arguments. Appl. Math. Lett. 20, 43–47 (2007) CrossRefMATHMathSciNet Zong, M., Liang, H.: Periodic solutions for Rayleigh type p-Laplacian equation with deviating arguments. Appl. Math. Lett. 20, 43–47 (2007) CrossRefMATHMathSciNet
20.
Zurück zum Zitat Gao, F., Lu, S., Zhang, W.: Periodic solutions for a Rayleigh type p-Laplacian equation with sign-variable coefficient of nonlinear term. Appl. Math. Comput. 216, 2010–2015 (2010) CrossRefMATHMathSciNet Gao, F., Lu, S., Zhang, W.: Periodic solutions for a Rayleigh type p-Laplacian equation with sign-variable coefficient of nonlinear term. Appl. Math. Comput. 216, 2010–2015 (2010) CrossRefMATHMathSciNet
21.
Zurück zum Zitat He, Z., Wang, W., Yi, X.: Existence and uniqueness of periodic solutions for Rayleigh type p-Laplacian equation. J. Comput. Appl. Math. 232, 558–564 (2009) CrossRefMATHMathSciNet He, Z., Wang, W., Yi, X.: Existence and uniqueness of periodic solutions for Rayleigh type p-Laplacian equation. J. Comput. Appl. Math. 232, 558–564 (2009) CrossRefMATHMathSciNet
22.
Zurück zum Zitat Zhou, Y., Tang, X.: Periodic solutions for a kind of Rayleigh equation with a deviating argument. Comput. Math. Appl. 53, 825–830 (2007) CrossRefMATHMathSciNet Zhou, Y., Tang, X.: Periodic solutions for a kind of Rayleigh equation with a deviating argument. Comput. Math. Appl. 53, 825–830 (2007) CrossRefMATHMathSciNet
23.
Zurück zum Zitat Xiao, B., Liu, B.: Periodic solutions for Rayleigh type p-Laplacian equation with a deviating argument. Nonlinear Anal., Real World Appl. 10, 16–22 (2009) CrossRefMATHMathSciNet Xiao, B., Liu, B.: Periodic solutions for Rayleigh type p-Laplacian equation with a deviating argument. Nonlinear Anal., Real World Appl. 10, 16–22 (2009) CrossRefMATHMathSciNet
24.
Zurück zum Zitat Xiong, W., Shao, J.: Existence and uniqueness of positive periodic solutions for Rayleigh type p-Laplacian equation. Nonlinear Anal., Real World Appl. 10, 1343–1350 (2009) CrossRefMATHMathSciNet Xiong, W., Shao, J.: Existence and uniqueness of positive periodic solutions for Rayleigh type p-Laplacian equation. Nonlinear Anal., Real World Appl. 10, 1343–1350 (2009) CrossRefMATHMathSciNet
25.
Zurück zum Zitat Gaines, R.E., Mawhin, J.L.: Coincidence Degree and Nonlinear Differential Equations. Springer, Berlin (1977) MATH Gaines, R.E., Mawhin, J.L.: Coincidence Degree and Nonlinear Differential Equations. Springer, Berlin (1977) MATH
26.
Zurück zum Zitat Wang, D.: Positive periodic solutions for a nonautonomous neutral delay prey-predator model with impulse and Hassell-Varley type functional response. Proc. Am. Math. Soc., in press Wang, D.: Positive periodic solutions for a nonautonomous neutral delay prey-predator model with impulse and Hassell-Varley type functional response. Proc. Am. Math. Soc., in press
Metadaten
Titel
Existence and uniqueness of periodic solution for prescribed mean curvature Rayleigh type p-Laplacian equation
verfasst von
Dongshu Wang
Publikationsdatum
01.10.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2014
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-013-0745-2

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