Existence and nonexistence of radial positive solutions of superlinear elliptic systems.

Ahammou, Abdelaziz. "Existence and nonexistence of radial positive solutions of superlinear elliptic systems.." Publicacions Matemàtiques 45.2 (2001): 399-419. <http://eudml.org/doc/41435>.

@article{Ahammou2001,
abstract = {The main goal in this paper is to prove the existence of radial positive solutions of the quasilinear elliptic system⎧ -Δpu = f(x,u,v) in Ω,⎨ -Δqv = g(x,u,v) in Ω,⎩ u = v = 0 on ∂Ω,where Ω is a ball in RN and f, g are positive continuous functions satisfying f(x, 0, 0) = g(x, 0, 0) = 0 and some growth conditions which correspond, roughly speaking, to superlinear problems. Two different sets of conditions, called strongly and weakly coupled, are given in order to obtain existence. We use the topological degree theory combined with the blow up method of Gidas and Spruck. When Ω = RN, we give some sufficient conditions of nonexistence of radial positive solutions for Liouville systems.},
author = {Ahammou, Abdelaziz},
journal = {Publicacions Matemàtiques},
keywords = {Ecuaciones diferenciales elípticas; Teorema de existencia; p-Laplacian; superlinear; radial solutions; blow-up arguments; topological degree},
language = {eng},
number = {2},
pages = {399-419},
title = {Existence and nonexistence of radial positive solutions of superlinear elliptic systems.},
url = {http://eudml.org/doc/41435},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Ahammou, Abdelaziz
TI - Existence and nonexistence of radial positive solutions of superlinear elliptic systems.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 2
SP - 399
EP - 419
AB - The main goal in this paper is to prove the existence of radial positive solutions of the quasilinear elliptic system⎧ -Δpu = f(x,u,v) in Ω,⎨ -Δqv = g(x,u,v) in Ω,⎩ u = v = 0 on ∂Ω,where Ω is a ball in RN and f, g are positive continuous functions satisfying f(x, 0, 0) = g(x, 0, 0) = 0 and some growth conditions which correspond, roughly speaking, to superlinear problems. Two different sets of conditions, called strongly and weakly coupled, are given in order to obtain existence. We use the topological degree theory combined with the blow up method of Gidas and Spruck. When Ω = RN, we give some sufficient conditions of nonexistence of radial positive solutions for Liouville systems.
LA - eng
KW - Ecuaciones diferenciales elípticas; Teorema de existencia; p-Laplacian; superlinear; radial solutions; blow-up arguments; topological degree
UR - http://eudml.org/doc/41435
ER -