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


Tokmak F., Karaca I. Y.

Abstract and Applied Analysis, vol.2012, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2012
  • Publication Date: 2012
  • Doi Number: 10.1155/2012/506716
  • Journal Name: Abstract and Applied Analysis
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Gazi University Affiliated: No

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. Copyright © 2012 Fatma Tokmak and Ilkay Yaslan Karaca.