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Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations

Abstract

The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space. The solutions will be obtained in a subspace of the Sobolev space. The proofs rely essentially on the Mountain Pass theorem and on Ekeland's Variational principle.

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Correspondence to Mihai Mihăilescu.

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Mihăilescu, M. Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations. Bound Value Probl 2006, 41295 (2006). https://doi.org/10.1155/BVP/2006/41295

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Weak Solution
  • Functional Equation