Elliptic equations involving the -Laplacian and a gradient term having natural growth

  • Djairo Guedes de Figueiredo

    IMECC - UNICAMP, Campinas, Brazil
  • Jean-Pierre Gossez

    Université Libre de Bruxelles, Belgium
  • Humberto Ramos Quoirin

    Universidad de Santiago de Chile, Chile
  • Pedro Ubilla

    Universidad de Santiago de Chile, Chile
Elliptic equations involving the $p$-Laplacian and a gradient term having natural growth cover

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Abstract

We investigate the problem

in a bounded smooth domain . Using a Kazdan–Kramer change of variable we reduce this problem to a quasilinear one without gradient term and therefore approachable by variational methods. In this way we come to some new and interesting problems for quasilinear elliptic equations which are motivated by the need to solve . Among other results, we investigate the validity of the Ambrosetti–Rabinowitz condition according to the behavior of and . Existence and multiplicity results for are established in several situations.

Cite this article

Djairo Guedes de Figueiredo, Jean-Pierre Gossez, Humberto Ramos Quoirin, Pedro Ubilla, Elliptic equations involving the -Laplacian and a gradient term having natural growth. Rev. Mat. Iberoam. 35 (2019), no. 1, pp. 173–194

DOI 10.4171/RMI/1052