## Differential and Integral Equations

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

M. A. S. Souto

#### 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

#### 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