Existence of Positive Solutions to Singular p-Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity

Abstract

By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an $m$-point singular $p$-Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential ($𝕋=ℝ$) and difference equations ($𝕋=\mathbb{Z}$), as well as in general time scales setting. As an application, an example is given to illustrate the results.