Time-Scale-Dependent Criteria for the Existence of Positive Solutions to p-Laplacian Multipoint Boundary Value Problem

Abstract

By virtue of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem, we analytically establish several sufficient criteria for the existence of at least two or three positive solutions in the p-Laplacian dynamic equations on time scales with a particular kind of p-Laplacian and m-point boundary value condition. It is this kind of boundary value condition that leads the established criteria to be dependent on the time scales. Also we provide a representative and nontrivial example to illustrate a possible application of the analytical results established. We believe that the established analytical results and the example together guarantee the reliability of numerical computation of those p-Laplacian and m-point boundary value problems on time scales.