Existence of positive solutions for third-order \(m\)-point boundary value problems with sign-changing nonlinearity on time scales (Q1938219)

Summary: 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.