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A Multiplicity Result for an Elliptic Anisotropic Differential Inclusion Involving Variable Exponents

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Abstract

In this paper we are concerned with the study of a class of quasilinear elliptic differential inclusions involving the anisotropic \(\overrightarrow {p}(\cdot)\)-Laplace operator, on a bounded open subset of \({\mathbb R}^n\) which has a smooth boundary. The abstract framework required to study this kind of differential inclusions lies at the interface of three important branches in analysis: nonsmooth analysis, the variable exponent Lebesgue–Sobolev spaces theory and the anisotropic Sobolev spaces theory. Using the concept of nonsmooth critical point we are able to prove that our problem admits at least two non-trivial weak solutions.

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Authors and Affiliations

  1. Research group of the project PD-3-0032, “Simion Stoilow” Institute of Mathematics of the Romanian Academy, Calea Grivitei 21, 010702, Bucharest, Romania

    Nicuşor Costea

  2. Department of Mathematics and its Applications, Central European University, Nador u. 9, 1051, Budapest, Hungary

    Nicuşor Costea & Gheorghe Moroşanu

Authors
  1. Nicuşor Costea
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  2. Gheorghe Moroşanu
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Correspondence to Nicuşor Costea.

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Costea, N., Moroşanu, G. A Multiplicity Result for an Elliptic Anisotropic Differential Inclusion Involving Variable Exponents. Set-Valued Var. Anal 21, 311–332 (2013). https://doi.org/10.1007/s11228-012-0224-1

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  • DOI: https://doi.org/10.1007/s11228-012-0224-1

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