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Open Access Research

Multiplicity of solutions for nonlinear impulsive differential equations with Dirichlet boundary conditions

Chenxing Zhou1, Fenghua Miao1 and Sihua Liang12*

Author Affiliations

1 College of Mathematics, Changchun Normal University, Changchun, Jilin, 130032, P.R. China

2 Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, P.R. China

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Boundary Value Problems 2013, 2013:200  doi:10.1186/1687-2770-2013-200

Published: 5 September 2013

Abstract

In this paper, we consider the existence of solutions for nonlinear impulsive differential equations with Dirichlet boundary conditions. Infinitely many solutions are obtained by using a version of the symmetric mountain-pass theorem, and this sequence of solutions converge to zero. Some recent results are extended.

MSC: 34B37, 35B38.

Keywords:
impulsive effects; variational methods; Dirichlet boundary value problem; critical points