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

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  • Fatma Tokmak
  • Ilkay Yaslan Karaca

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.

Suggested Citation

  • Fatma Tokmak & Ilkay Yaslan Karaca, 2012. "Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, December.
    • Handle: RePEc:hin:jnlaaa:506716
    DOI: 10.1155/2012/506716
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