Browse > Article

EXISTENCE OF THREE POSITIVE PERIODIC SOLUTIONS OF NEUTRAL IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS  

Liu, Yuji (Department of Mathematics, Guangdong University of Business Studies)
Xia, Jianye (Department of Mathematics, Guangdong University of Finance)
Publication Information
Journal of applied mathematics & informatics / v.28, no.1_2, 2010 , pp. 243-256 More about this Journal
Abstract
This paper is concerned with the neutral impulsive functional differential equations $$\{{x Sufficient conditions for the existence of at least three positive T-periodic solution are established. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results.
Keywords
Positive periodic solution; neutral impulsive functional differential equation; fixed-point theorem;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. Liu, L. Huang, Existence and uniqueness of periodic for a kind of first order neutral functional differential equations, J. Math. Anal. Appl., 322(2006), 121-132.   DOI   ScienceOn
2 R. Hakl, A. Lomtatidze, B. Puza, On periodic solutions 0f first order linear functional differential equations, Nonl. Anal., 49(2002), 929-945.   DOI   ScienceOn
3 S. Padhi, S. Srivastava, Multiple periodic solutions for a nonlinear first order functional differential equations with applications to population dynamics, Appl. Math. Comput., 203(2008), 1-6.   DOI   ScienceOn
4 X.H. Tang, Z. Jiang, Periodic solutions of first-order nonlinear functional differential equations, Nonl. Anal., 68(2008), 845-861.   DOI   ScienceOn
5 X. Han, S. Ji, Z. Ma, On the existence and multiplicity of positive periodic solutions for first-order vector differential equation, J. Math. Anal. Appl., 329(2007), 977-986.   DOI   ScienceOn
6 D. Bai, Y. Xu, Periodic solutions of first order functional differential equations with periodic deviations, Comput. Math. Appl., 53(2007), 1361-1366.   DOI   ScienceOn
7 G. Wang, Existence theorem of periodic solutions for a delay nonlinear differential equation with piecewise constant arguments, J. Math. Anal. Appl., 298(2004), 298-307.   DOI   ScienceOn
8 A. Cabada, J.B. Ferreiro, J.J. Nieto, Green's function and comparinciples for first order periodic differential equations with piecewise constant arguments, J. Math. Anal. Appl., 291(2004), 690-697.   DOI   ScienceOn
9 D. Li, Y. Xu, Existence of periodic solutions for fully nonlinear first-order differential equations, Nonl. Anal., 52(2003), 1095-1109.   DOI   ScienceOn
10 Ch. G. Philos, I. K. Purnaras, Periodic first order linear neutral delay differential equations, Appl. Math. Comput., 117(2001), 203-222.   DOI   ScienceOn
11 S. Kang, G. Zhang, B. Shi, Existence of three periodic positive solutions for a class of integral equations with parameters, J. Math. Anal. Appl., 323(2006), 654-665.   DOI   ScienceOn
12 Y. Liu, Positive periodic solutions of nonlinear differential equations, Applied Mathematics A Journal of Chinese Universities, B(4) (2003), 1-5.
13 J. Yu, B. Liu, Existence of periodic solutions 10r nonlinear neutral delay differential equations, Applied Mathematics A Journal of Chinese Universities, A(3)(2001), 11-15.
14 Y. Liu, W. Ge, Stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients, Nonl. Anal., 57(2004), 363-399.   DOI   ScienceOn
15 X. Li, X. Lin, D. Jiang, X. Zhang, Existence and multiplicity of positive periodic solutions to 1unctional differential equations with impulse effects, Nonl. Anal., 62 (2005), 683-701.   DOI   ScienceOn
16 G. S. Ladde, V. Lakshmikantham, A. S. Vatsala, Monotone iterative techniques for nonlinear differential equations, Pitman Advanced Publishing Program, 1985.
17 X. Fan, Y. Li, Positive periodic solutions of neutral functional differential equations with a parameter and impulse, Electronic J. of Differential Equations, 38(2008), 1-8.
18 J. Yan, Existence of positive periodic solutions of impulsive functional differential equations with two parameters, J. Math. Anal. Appl , 327(2007), 854-868.   DOI   ScienceOn
19 S. Cheng, G. Zhang, Existence of positive periodic solutions for non-autonomous functional differential equations, Electron J. Diff. Eqns., 59(2001), 1-8.
20 J. O. Alzabut, A necessary and sufficient conditions for the existence of periodic solutions of linear impulsive distributed delay, Discrete and Continuous Dynamical Systems, Website: www.AIMSciences.org, 15 (2007), 35-43.
21 S. Kang, G. Zhang, Existence of nontrivial periodic solutions for first order functional differential equations, Appl. Math. Letters, 18(2005), 101-107.   DOI   ScienceOn