Open Access Research

Study on integro-differential equation with generalized p-Laplacian operator

Li Wei1, Ravi P Agarwal23* and Patricia JY Wong4

Author Affiliations

1 School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061, China

2 Department of Mathematics, Texas A&M University — Kingsville, Kingsville, TX, 78363, USA

3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

4 School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

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Boundary Value Problems 2012, 2012:131  doi:10.1186/1687-2770-2012-131

Published: 13 November 2012

Abstract

We tackle the existence and uniqueness of the solution for a kind of integro-differential equations involving the generalized p-Laplacian operator with mixed boundary conditions. This is achieved by using some results on the ranges for maximal monotone operators and pseudo-monotone operators. The method used in this paper extends and complements some previous work.

MSC: 47H05, 47H09.

Keywords:
maximal monotone operator; pseudo-monotone operator; generalized p-Laplacian operator; integro-differential equation; mixed boundary conditions