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Concentration phenomena in nonlinear eigenvalue problems with variable exponents and sign-changing potential

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Abstract

In this paper we establish the concentration of the spectrum in an unbounded interval for a class of eigenvalue problems involving variable growth conditions and a sign-changing potential. We also study the optimization problem for the particular eigenvalue given by the infimum of the associated Rayleigh quotient when the variable potential lies in a bounded, closed and convex subset of a certain variable exponent Lebesgue space.

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Authors and Affiliations

  1. Department of Mathematics, University of Craiova, 200585, Craiova, Romania

    Mihai Mihăilescu & Vicenţiu Rădulescu

  2. Department of Mathematics, Central European University, 1051, Budapest, Hungary

    Mihai Mihăilescu

  3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Vicenţiu Rădulescu

Authors
  1. Mihai Mihăilescu
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  2. Vicenţiu Rădulescu
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Correspondence to Mihai Mihăilescu.

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Mihăilescu, M., Rădulescu, V. Concentration phenomena in nonlinear eigenvalue problems with variable exponents and sign-changing potential. JAMA 111, 267–287 (2010). https://doi.org/10.1007/s11854-010-0018-z

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  • DOI: https://doi.org/10.1007/s11854-010-0018-z

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