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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 506716, 15 pages
http://dx.doi.org/10.1155/2012/506716
Research Article

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

Department of Mathematics, Ege University, Izmir, 35100 Bornova, Turkey

Received 2 August 2012; Accepted 8 November 2012

Academic Editor: Yongfu Su

Copyright © 2012 Fatma Tokmak and Ilkay Yaslan Karaca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 -point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual -Laplacian operator. In particular, the nonlinear term is allowed to change sign. As an application, we also give some examples to demonstrate our results.