Geodesic
Perturbed nonlinear degenerate problems in $\mathbb R^N $
A. El Khalil1 ; S. El Manouni1 ; M. Ouanan2
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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
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

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 
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A. El Khalil; S. El Manouni; M. Ouanan. Perturbed nonlinear degenerate problems in $\mathbb R^N $. Applicationes Mathematicae, Tome 36 (2009) no. 2, pp. 213-223. doi : 10.4064/am36-2-8. http://geodesic.mathdoc.fr/articles/10.4064/am36-2-8/

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