Existence of multiple positive solutions for p-Laplacian multipoint boundary value problems on time scales

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Dogan A.

ADVANCES IN DIFFERENCE EQUATIONS, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-1847-2013-238
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: time scales, boundary value problem, p-Laplacian, positive solutions, fixed point theorem, SIGN CHANGING NONLINEARITY, M-POINT BVP, DYNAMIC EQUATIONS, INCREASING HOMEOMORPHISM, HOMOMORPHISM
  • Abdullah Gül University Affiliated: Yes

Abstract

In this paper, we consider p-Laplacian multipoint boundary value problems on time scales. By using a generalization of the Leggett-Williams fixed point theorem due to Bai and Ge, we prove that a boundary value problem has at least three positive solutions. Moreover, we study existence of positive solutions of a multipoint boundary value problem for an increasing homeomorphism and homomorphism on time scales. By using fixed point index theory, sufficient conditions for the existence of at least two positive solutions are provided. Examples are given to illustrate the results.