Veuillez utiliser cette adresse pour citer ce document : http://dspace.univ-tlemcen.dz/handle/112/1871
Titre: Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary
Auteur(s): ABDELLAOUI, Boumediene
GIACHETTI, Daniela
PERAL, Ireneo
WALIAS, Magdalena
Mots-clés: Elliptic equations
Singular nonlinearities
Dependence on the gradient
Date de publication: 15-fév-2011
Résumé: In this paper we consider the problem{-Delta u = u(q alpha)vertical bar del u vertical bar(q) +lambda f(x) in Omega u = 0 on partial derivative Omega , (P)where Omega subset of R(N) is a bounded domain, 1 < q <= 2, alpha is an element of R and f >= 0. We prove that:(1) If q alpha < -1, then problem (P) has a distributional solution for all f is an element of L(1)(Omega), and all lambda > 0.(2) If -1 <= q alpha < 0, then problem (P) has a solution for all f is an element of L(s)(Omega), where s > N/q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q&#n;q if N&#xnN >= 2, and without any restriction on lambda.(3) If q = 2 and -1 <= q alpha < 0 then problem (P) has infinitely many solutions under suitable hypotheses on f.(4) If 0 <= q alpha and f is an element of L(1)(Omega) satisfieslambda 1 (f) = inf (phi is an element of W01,2(Omega)) integral(Omega)vertical bar del phi vertical bar(2)dx/integral(Omega)f phi(2)dx > 0,then problem (P) has a positive solution if 0 < lambda < lambda(1)(f) and no positive solution for large lambda.
Description: Nonlinear Analysis: Theory, Methods & Applications, ISSN : 0362-546X, DOI : 10.1016/j.na.2010.10.008, Issue : 4, Volume : 74, pp. 1355–1371, 15 February 2011.
URI/URL: http://dspace.univ-tlemcen.dz/handle/112/1871
ISSN: 0362-546X
Collection(s) :Articles internationaux

Fichier(s) constituant ce document :
Fichier Description TailleFormat 
Elliptic-problems-with-nonlinear-terms-depending-on-the-gradient.pdf93,74 kBAdobe PDFVoir/Ouvrir


Tous les documents dans DSpace sont protégés par copyright, avec tous droits réservés.