Basic Theory of Nonlinear Third-Order q-Difference Equations and Inclusions

Abstract

We investigate the existence of solutions for boundary value problems of the third-order q-difference equations and inclusions. Our results are based on some standard fixed point theorems. In case of inclusion problem, the existence results are obtained for convex as well as nonconvex multi-valued maps. We also discuss the existence of extremal solutions for the inclusion problem.

Keywords:

• q-difference equations
• inclusions
• fixed point
• extremal solution

AMS Subject Classification:

• 34A60
• 39A13