Translator Disclaimer
1998 Existence and uniqueness of positive solutions to certain differential systems
Patricio Felmer, Salomé Martínez
Adv. Differential Equations 3(4): 575-593 (1998).

Abstract

In this article we study existence and uniqueness of positive solutions for elliptic systems of the form $$ \begin{align} -\Delta v = &f(x,u) \quad \hbox{in} \quad \Omega \\ -\Delta u = & v^\beta \quad \hbox{in}\quad \Omega, \end{align} $$ with Dirichlet boundary condition on a bounded smooth domain in $\Bbb R^N$. The nonlinearity $f$ is assumed to have a sub-$\beta$ growth with $\beta>0$, that in case $f(x,u)=u^\alpha, \alpha>0$, corresponds to $\alpha\beta<1$. The results are also valid for a larger class of systems, including some infinite dimensional Hamiltonian Systems.

Citation

Download Citation

Patricio Felmer. Salomé Martínez. "Existence and uniqueness of positive solutions to certain differential systems." Adv. Differential Equations 3 (4) 575 - 593, 1998.

Information

Published: 1998
First available in Project Euclid: 18 April 2013

zbMATH: 0946.35028
MathSciNet: MR1659242

Subjects:
Primary: 35J55
Secondary: 35B05, 35J65

Rights: Copyright © 1998 Khayyam Publishing, Inc.

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.3 • No. 4 • 1998
Back to Top