Open Access Research

Eigenvalue criteria for existence of positive solutions of impulsive differential equations with non-separated boundary conditions

Ruixi Liang1* and Jianhua Shen2

Author Affiliations

1 Department of Mathematics and Statistics, Central South University, Changsha, Hunan, 410075, P.R. China

2 Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang, 310036, P.R. China

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Boundary Value Problems 2013, 2013:3 doi:10.1186/1687-2770-2013-3

Published: 14 January 2013

Abstract

In this paper, we discuss the existence of positive solutions for second-order differential equations subject to nonlinear impulsive conditions and non-separated periodic boundary value conditions. Our criteria for the existence of positive solutions will be expressed in terms of the first eigenvalue of the corresponding nonimpulsive problem. The main tool of study is a fixed point theorem in a cone.

MSC: 34B37, 34B18.

Keywords:
impulsive differential equation; positive solution; fixed point theorem; non-separated periodic boundary value condition