Existence of Positive Solutions for Third‐Order m‐Point Boundary Value Problems with Sign‐Changing Nonlinearity on Time Scales
Articles > Article · 2012
Authors: Fatma Tokmak, İlkay KARACA
Abstract and Applied Analysis, Journal Indexed in SCI Expanded, International, WoS, 2012, vol 2012, pp 1-15
DOI: 10.1155/2012/506716
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.