Quasilinear problems involving a perturbation with quadratic growth in the gradient and a noncoercive zeroth order term
Boussad Hamour
Ecole Normale Supérieure, Alger, AlgeriaFrançois Murat
Université Pierre et Marie Curie, Paris, France
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Abstract
In this paper we consider the problem
where is an open bounded set of , , is a coercive matrix with coefficients in , is a Carathéodory function which satisfies for some
belongs to and to , . For and sufficiently small, we prove the existence of at least one solution of this problem which is such that belongs to for some . This solution satisfies some a priori estimate.
Cite this article
Boussad Hamour, François Murat, Quasilinear problems involving a perturbation with quadratic growth in the gradient and a noncoercive zeroth order term. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 2, pp. 195–233
DOI 10.4171/RLM/731