Open Access Research

Periodic boundary value problems for second-order impulsive integro-differential equations with integral jump conditions

Chatthai Thaiprayoon1,2*, Decha Samana1,2 and Jessada Tariboon2,3

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Author affiliations

1 Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand

2 Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok, 10400, Thailand

3 Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

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Citation and License

Boundary Value Problems 2012, 2012:122 doi:10.1186/1687-2770-2012-122

Published: 24 October 2012

Abstract

This paper is concerned with the existence of extremal solutions of periodic boundary value problems for second-order impulsive integro-differential equations with integral jump conditions. We introduce a new definition of lower and upper solutions with integral jump conditions and prove some new maximum principles. The method of lower and upper solutions and the monotone iterative technique are used.

MSC: 34B37, 34K10, 34K45.

Keywords:
impulsive integro-differential equation; lower and upper solutions; periodic boundary value problem; monotone iterative technique