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1995 A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems
M. A. S. Souto
Differential Integral Equations 8(5): 1245-1258 (1995).

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 $1 <pq <\sigma < (N+2)/(N-2).$

Citation

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M. A. S. Souto. "A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems." Differential Integral Equations 8 (5) 1245 - 1258, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0823.35064
MathSciNet: MR1325555

Subjects:
Primary: 35J60
Secondary: 35B05, 35B45, 35J55

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 5 • 1995
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