Differential and Integral Equations

A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems

M. A. S. Souto

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study the existence of positive solutions for elliptic systems of the form (1) below, when $f$ has asymptotic behavior at $+\infty$ as $u^\sigma$ and $g$ satisfies some subcritical growth. Our result guarantees a nontrivial solution $(u,v)$ to the system $$ -\Delta u = u^\sigma + v^q,\;\;\; -\Delta v = u^p \quad \text {in} \quad \Omega; \quad u=v=0 \quad \text {on} \quad \partial \Omega, $$ where $1 <pq <\sigma < (N+2)/(N-2).$

Article information

Source
Differential Integral Equations, Volume 8, Number 5 (1995), 1245-1258.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369056053

Mathematical Reviews number (MathSciNet)
MR1325555

Zentralblatt MATH identifier
0823.35064

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B45: A priori estimates 35J55

Citation

Souto, M. A. S. A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems. Differential Integral Equations 8 (1995), no. 5, 1245--1258. https://projecteuclid.org/euclid.die/1369056053


Export citation