EXISTENCE OF DISSIPATIVE-AFFINE-PERIODIC SOLUTIONS FOR DISSIPATIVE-AFFINE-PERIODIC SYSTEMS

Moxin Liu; Fei Xu; Xue Yang; Yong Li

doi:10.11948/2017099

2017 Volume 7 Issue 4

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Moxin Liu, Fei Xu, Xue Yang, Yong Li. EXISTENCE OF DISSIPATIVE-AFFINE-PERIODIC SOLUTIONS FOR DISSIPATIVE-AFFINE-PERIODIC SYSTEMS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1624-1636. doi: 10.11948/2017099

Citation:

Moxin Liu, Fei Xu, Xue Yang, Yong Li. EXISTENCE OF DISSIPATIVE-AFFINE-PERIODIC SOLUTIONS FOR DISSIPATIVE-AFFINE-PERIODIC SYSTEMS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1624-1636. doi: 10.11948/2017099

EXISTENCE OF DISSIPATIVE-AFFINE-PERIODIC SOLUTIONS FOR DISSIPATIVE-AFFINE-PERIODIC SYSTEMS

1 School of Mathematics, Jilin University, 2699 Qianjin Street, 130012 Changchun, China;
2 School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, 130024 Changchun, China;
3 Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, 2555 Jingyue Street, 130117 Changchun, China

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Abstract

Abstract

In this paper, we prove that every first order dissipative-(T,a)-affine-periodic system admits a dissipative-(T,a)-affine-periodic solution in[0,∞) via the Leray-Schauder degree theory and the lower and upper solutions method.
- Dissipative-affine-periodic solution /
- dissipative-affine-periodic system /
- existence
MSC: 34B15;34C25

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References

[1]	X. Chang and Y. Li, Rotating periodic solutions of second order dissipative dynamical systems, Discrete Contin. Dyn. Syst., 2016, 36(2), 643-652. Google Scholar
[2]	C. Cheng, F. Huang and Y. Li, Affine-periodic solutions and pseudo affineperiodic solutions for differential equations with exponential dichotomy and exponential trichotomy, J. Appl. Anal. Comput., 2016, 6(4), 950-967. Google Scholar
[3]	C. De Coster and P. Habets, Two-point boundary value problems:lower and upper solutions, Mathematics in Science and Engineering, 205. Elsevier B. V., Amsterdam, 2006. xii+489 pp. Google Scholar
[4]	C. Fabry and P. Habets, The Picard boundary value problem for nonlinear second order vector differential equations, J. Differential Equations, 1981, 42(2), 186-198. Google Scholar
[5]	F. A. Howes, Differential inequalities of higher order and the asymptotic solution of nonlinear boundary value problems, SIAM J. Math. Anal., 1982, 13(1), 61-80. Google Scholar
[6]	T. Küpper, Y. Li and B. Zhang, Periodic solutions for dissipative-repulsive systems, Tohoku Math. J. (2), 2000, 52(3), 321-329. Google Scholar
[7]	N. Levinson, Transformation theory of non-linear differential equations of the second order, Ann. of Math. (2), 1944, 45, 723-737. Google Scholar
[8]	Y. Li and F. Huang, Levinson's problem on affine-periodic solutions, Adv. Nonlinear Stud., 2015, 15(1), 241-252. Google Scholar
[9]	Z. Liu and W. Wang, Favard separation method for almost periodic stochastic differential equations, J. Differential Equations, 2016, 260(11), 8109-8136. Google Scholar
[10]	X. Meng and Y. Li, Affine-periodic solutions for discrete dynamical systems, J. Appl. Anal. Comput., 2015, 5(4), 781-792. Google Scholar
[11]	J. J. Nieto, Periodic solutions for third order ordinary differential equations, Comment. Math. Univ. Carolin., 1991, 32(3), 495-499. Google Scholar
[12]	E. Picard, Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires, Journal de Mathématiques Pures et Appliquées, 1893, 9, 217-272. Google Scholar
[13]	C. Wang and Y. Li, Affine-periodic solutions for nonlinear dynamic equations on time scales, Adv. Difference Equ, 2015. DOI:10.1186/s13662-015-0634-0. Google Scholar
[14]	C. Wang, X. Yang and Y. Li, Affine-periodic solutions for nonlinear differential equations, Rocky Mountain J. Math., 2016, 46(5), 1717-1737. Google Scholar
[15]	H. Wang, X. Yang and Y. Li, Rotating-symmetric solutions for nonlinear systems with symmetry, Acta Math. Appl. Sin. Engl. Ser., 2015, 31(2), 307-312. Google Scholar
[16]	R. Wu, An anti-periodic LaSalle oscillation theorem, Appl. Math. Lett., 2008, 21(9), 928-933. Google Scholar
[17]	R. Wu, The existence of T-anti-periodic solutions, Appl. Math. Lett., 2010, 23(9), 984-987. Google Scholar
[18]	R. Wu, F. Cong and Y. Li, Anti-periodic solutions for second order differential equations, Appl. Math. Lett., 2011, 24(6), 860-863. Google Scholar
[19]	F. Xu, Y. Li, Y. Gao and X. Xu, The well-posedness of fractional systems with affine-periodic boundary conditions, Differential Equations and Dynamical Systems, 2017. DOI:10.1007/s12591-017-0360-z. Google Scholar
[20]	Y. Zhang, X. Yang and Y. Li, Affine-periodic solutions for dissipative systems, Abstr. Appl. Anal, 2013. DOI:10.1155/2013/157140. Google Scholar