In this article we study the problem (P)\quad \left\{ \begin{array}{rcl} -\Delta u+|\grad u|^q=\lambda g(x)u+f(x)\inn\Omega, u>0\inn\O, u=0\onn\partial\Omega, with 1\le q\le 2 and f, g are positive measurable functions. We give assumptions on g with respect to q for which for all \lambda>0 and all f\in L^1, f\ge 0, problem (P) has a positive solution. In particular we focus our attention on g(x)=\dfrac 1{|x|^2} to prove that the assumptions on g are optimal.
Abdellaoui, B., Peral, I., & Primo Ramos, A. (2008). Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 25(5), 969-985.
Citazione: | Abdellaoui, B., Peral, I., & Primo Ramos, A. (2008). Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 25(5), 969-985. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations |
Autori: | Abdellaoui, B; Peral, I; Primo Ramos, A |
Autori: | |
Data di pubblicazione: | 2008 |
Lingua: | English |
Rivista: | ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.anihpc.2007.06.003 |
Appare nelle tipologie: | 01 - Articolo su rivista |