Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales

Tokmak F., Karaca I. Y.

Boundary Value Problems, vol.2013, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-2770-2013-52
  • Journal Name: Boundary Value Problems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Fixed-point theorem, Increasing homeomorphism and homomorphism, M-point boundary value problem, Symmetric positive solution, Time scales
  • Gazi University Affiliated: No

Abstract

In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that the considered equation admits a nonlinear term f whose sign is allowed to change. The discussed problem involves both an increasing homeomorphism and homomorphism, which generalizes the p-Laplacian operator. An example which supports our theoretical results is also indicated. © 2013 Gao and Gao; licensee Springer.