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Existence of solutions for quasilinear elliptic equations with jumping nonlinearities under the Neumann boundary condition

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Abstract

By variational methods, we prove the existence of a non-trivial solution for the quasilinear elliptic equations with jumping nonlinearities under the Neumann boundary condition. We also provide existence results for positive, negative and non-trivial multiple solutions. The studied equations contain the p-Laplacian problems as a special case.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Perpignan, 52 Avenue Paul Alduy, 66860, Perpignan, France

    Dumitru Motreanu

  2. Department of Mathematics, Tokyo University of Science, Kagurazaka 1-3, Shinjyuku-ku, Tokyo, 162-8601, Japan

    Mieko Tanaka

Authors
  1. Dumitru Motreanu
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  2. Mieko Tanaka
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Correspondence to Dumitru Motreanu.

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Communicated by P. Rabinowitz.

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Motreanu, D., Tanaka, M. Existence of solutions for quasilinear elliptic equations with jumping nonlinearities under the Neumann boundary condition. Calc. Var. 43, 231–264 (2012). https://doi.org/10.1007/s00526-011-0410-2

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  • DOI: https://doi.org/10.1007/s00526-011-0410-2

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