Existence of Positive Solutions for Third-Order m -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

Abstract

A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order $m$-point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual $p$-Laplacian operator. In particular, the nonlinear term $f(t,u)$ is allowed to change sign. As an application, we also give some examples to demonstrate our results.