Solvability for second order nonlinear impulsive boundary value problems

Dandan Yang,Gang Li

doi:10.14232/ejqtde.2009.1.41

Abstract

In this paper, we are concerned with the solvability for a class of second order nonlinear impulsive boundary value problem. New criteria are established based on Schaefer's fixed-point theorem. An example is presented to illustrate our main result. Our results essentially extend and complement some previous known results.

Highlights

Impulsive differential equations play a very important role in understanding mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology, economics and so on, see [1,2,8,10,17]
About wide applications of the theory of impulsive differential equations to different areas, we refer the readers to monographs [5,7,18,19] and the references therein
The authors studied the existence of solutions to the problem (1.1) in view of differential inequalities and Schaefer’s fixed-point theorem

Summary

Introduction

Impulsive differential equations play a very important role in understanding mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology, economics and so on, see [1,2,8,10,17]. Yuan in [4] studied the following first order impulsive nonlinear periodic boundary value problem. Where T > 0 and f : [0, T ] × Rn → Rn is continuous on (t, u) ∈ [0, T ] \ {t1} × Rn. The authors studied the existence of solutions to the problem (1.1) in view of differential inequalities and Schaefer’s fixed-point theorem. The authors studied the existence of solutions to the problem (1.1) in view of differential inequalities and Schaefer’s fixed-point theorem Their results extend those of [9,14] in the sense that they allow superlinear growth in nonlinearity f (t, p) in p. In 2007, Bai and Yang in [3] presented the existence results for the following second-order impulsive periodic boundary value problems. An example is given in the last section to demonstrate the application of our main result

Preliminaries

Main results

An example