﻿
 doi:

DOI: 10.3724/SP.J.1160.2013.00360

Acta Analysis Functionalis Applicata (应用泛函分析学报) 2013/15:4 PP.360-366

## Existence of Nontrivial Solutions for Second Order Impulsive Periodic Boundary Value Problems

• XU Jiafa 1   WEI Zhongli 1,2   DING Youzheng 1,2
• 1.School of Mathematics, Shandong University, Jinan 250100, China;
• 2.Department of Mathematics, Shandong Jianxhu University, Jinan 250101, China

Abstract：
In this paper,a class of second order periodic boundary value problem with impulsive effects is considered.The existence theorems of nontrivial solutions are obtained by virtue of variational methods and critical point theory.The results here extend the existing study.

Key words：periodic boundary value problem,impulse,variational method,critical point theory,nontrivial solution

ReleaseDate：2015-04-21 14:22:15

1 Zhang D,Dai B X. Infinitely many solutions for a class of nonlinear impulsive differential equations with periodic boundary conditions[J].Computers & Mathematics with Applications,2011.3153-3160.

2 Zhang D,Dai B X. Existence of solutions for nonlinear impulsive differential equations with Dirichlet boundary conditions[J].Mathematical and Computer Modelling,2011.1154-1161.

3 Nieto J J,O'Regan D. Variational approach to impulsive differential equations[J].Nonlinear Analysis:Real World Applications,2009.680-690.

4 Qian A X,Li C. Infinitely many solutions for a robin boundary value problem[J].International Journal of Differential Equations,2010.9.

5 Sun J T,Chen H B. Variational method to the impulsive equation with Neumann boundary conditions[J].Boundary Value Problems,2009.17.

6 Sun J T,Chen H B,Nieto J J. The multiplicity of solutions for perturbed second order Hamiltonian systems with impulsive effects[J].Nonlinear Analysis TMA,2010.4575-4586.

7 Sun J T,Chen H B,Nieto J J. Infinitely many solutions for second order Hamiltonian systems with impulsive effects[J].Mathematical and Computer Modelling,2011.544-555.

8 Tian Y,Ge W G,Yang D W. Existence results for second order system with impulsive effects via variational methods[J].Journal of Applied Mathematics and Computing,2009.255-265.

9 Xiao J,Nieto J J,Luo Z G. Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods[J].Commun Nonlinear Sci Numer Simulat,2012.426-432.

10 Chen H W,Li J L. Variational approach to impulsive differential equations with Dirichlet boundary conditions[J].Boundary Value Problems,2010.16.

11 Chen P,Tang X H. New existence and multiplicity of solutions for some Dirichlet problems with impulsive effects[J].Mathematical and Computer Modelling,2012.723-739.

12 Zhou J W,Li Y K. Existence of solutions for a class of second order Hamiltonian systems with impulsive effects[J].Nonlinear Analysis TMA,2010.1594-1603.

13 Zhou J W,Li Y K. Existence and Multiplicity of solutions for some Dirichlet problems with impulsive effects[J].Nonlinear Analysis TMA,2009.2856-2865.

14 Tian Y,Ge W G. Multiple positive solutions for periodic boundary value problem via variational methods[J].Tamkang Journal of Mathematics,2008.111-119.

15 Drábek P,Milota J. Methods of nonlinear analysis,applications to differential equations[M].Birkh(a)user Verlag AG Basel.Boston.Berlin,2007.

16 Willem M. Minimax theorems[M].Birkh(a)user,Boston,1996.

17 孙经先. 非线性泛函分析以及应用[M].北京:科学出版社,2008.