Perturbed nonlinear degenerate problems in $\mathbb R^N $

A. El Khalil ¹   ; S. El Manouni ¹   ; M. Ouanan ²

¹ Department of Mathematics Faculty of Sciences Al-Imam Muhammad ibn Saud Islamic University P.O. Box 90950 Riyadh 11623, Saudi Arabia
² Département d'Informatique Faculté des Sciences et Techniques Errachidia (FSTE) B.P. 509, Boutalamine 52000 Errachidia, Morocco

Applicationes Mathematicae, Tome 36 (2009) no. 2, pp. 213-223

Résumé

Via critical point theory we establish the existence and regularity of solutions for the quasilinear elliptic problem $$ \left\{\eqalign{ {-}\textrm{div} \mathcal{A}(x, \nabla u) + a(x)\vert u \vert^{p-2} u = g(x)|u|^{p-2}u + h(x)|u|^{s-1}u \quad\ \hbox{in } {\Bbb R}^N,\cr >0,\quad\ \lim_{\vert x \vert \rightarrow \infty} u(x) = 0,}\right. $$ where $ 1 p N $; $ a(x) $ is assumed to satisfy a coercivity condition; $ h(x)$ and $ g(x)$ are not necessarily bounded but satisfy some integrability restrictions.

Détail

DOI : 10.4064/am36-2-8

Keywords: via critical point theory establish existence regularity solutions quasilinear elliptic problem eqalign textrm div mathcal nabla vert vert p p s quad hbox bbb quad lim vert vert rightarrow infty right where assumed satisfy coercivity condition necessarily bounded satisfy integrability restrictions