New York Journal of Mathematics
Volume 7 (2001) 267-280


Abdelaziz Ahammou

Positive Radial Solutions of Nonlinear Elliptic Systems

Published: November 16, 2001
Keywords: Blow up argument, degree theory, Leray-Schauder theorem, excision property.
Subject: 35J25, 35J60

In this article, we are concerned with the existence of positive radial solutions of the problem (S+):
pu= f(x,u,v) in Ω,
qv= g(x,u,v) in Ω,
u = v = 0 on \partialΩ,
where Ω is a ball in RN and f, g are positive functions satisfying f(x,0,0)=g(x,0,0)=0. Under some growth conditions, we show the existence of a positive radial solution of the problem S+. We use traditional techniques of the topological degree theory. When Ω=RN, we give some sufficient conditions of nonexistence.

Author information

Département des Mathématiques et Informatique Faculté des Sciences UCD, El Jadida, BP20, Maroc