Open Access Research

Solutions to a boundary value problem of a fourth-order impulsive differential equation

Jingli Xie1 and Zhiguo Luo2*

Author affiliations

1 College of Mathematics and Statistics, Jishou University, Jishou, Hunan, 416000, P.R. China

2 Department of Mathematics, Hunan Normal University, Changsha, Hunan, 410081, P.R. China

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Citation and License

Boundary Value Problems 2013, 2013:154  doi:10.1186/1687-2770-2013-154

Published: 1 July 2013

Abstract

This paper is concerned with the existence of solutions to a boundary value problem of a fourth-order impulsive differential equation with a control parameter λ. By employing some existing critical point theorems, we find the range of the control parameter in which the boundary value problem admits at least one solution. It is also shown that under certain conditions there exists an interval of the control parameter in which the boundary value problem possesses infinitely many solutions. The main results are also demonstrated with examples.

MSC: 34B15, 34B18, 34B37, 58E30.

Keywords:
critical point theorem; impulsive differential equations; boundary value problem