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

Abstract EN

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.