On Existence of Solutions for Nonlinear q-difference Equations with Nonlocal q-integral Boundary Conditions

Ravi P. AgarwalTexas A&M University, Department of Mathematics, Texas A&M University, Kingsville, TX78363-8202, USA;King Abdulaziz University, NAAM-Research Group, Department of Mathematics, Faculty of Science, P.O. Box 80203, Jeddah21589, Saudi ArabiaCorrespondence[email protected]

Guotao WangShanxi Normal University, School of Mathematics and Computer Science, Linfen, Shanxi041004, People's Republic of China

Bashir AhmadKing Abdulaziz University, NAAM-Research Group, Department of Mathematics, Faculty of Science, P.O. Box 80203, Jeddah21589, Saudi Arabia

Lihong ZhangShanxi Normal University, School of Mathematics and Computer Science, Linfen, Shanxi041004, People's Republic of China

Aatef HobinyKing Abdulaziz University, NAAM-Research Group, Department of Mathematics, Faculty of Science, P.O. Box 80203, Jeddah21589, Saudi Arabia

Shatha MonaquelKing Abdulaziz University, NAAM-Research Group, Department of Mathematics, Faculty of Science, P.O. Box 80203, Jeddah21589, Saudi Arabia

Abstract

In this paper, we discuss the existence of solutions for nonlinear q-difference equations with nonlocal q-integral boundary conditions. The first part of the paper deals with some existence and uniqueness results obtained by means of standard tools of fixed point theory. In the second part, sufficient conditions for the existence of extremal solutions for the given problem are established. The results are well illustrated with the aid of examples.

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