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On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers

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  • Claudianor O. Alves
  • Marco A. S. Souto

Abstract

We prove that the semilinear elliptic equation , in , , on has a positive solution when the nonlinearity belongs to a class which satisfies at infinity and behaves like near the origin, where if and if . In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of .

Suggested Citation

  • Claudianor O. Alves & Marco A. S. Souto, 2008. "On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-6, June.
    • Handle: RePEc:hin:jnlaaa:578417
    DOI: 10.1155/2008/578417
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