Elliptic equations involving the -Laplacian and a gradient term having natural growth
Djairo Guedes de Figueiredo
IMECC - UNICAMP, Campinas, BrazilJean-Pierre Gossez
Université Libre de Bruxelles, BelgiumHumberto Ramos Quoirin
Universidad de Santiago de Chile, ChilePedro Ubilla
Universidad de Santiago de Chile, Chile
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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