Open Access
Translator Disclaimer
2001 Existence for an elliptic system with nonlinear boundary conditions via fixed-point methods
Julián Fernández Bonder, Julio D. Rossi
Adv. Differential Equations 6(1): 1-20 (2001).

Abstract

In this paper we prove the existence of nonnegative nontrivial solutions of the system $$\left\{\begin{array}{rcll} \Delta u & = & u & \mbox{in } \Omega,\\ \Delta v & = & v, & \end{array}\right.$$ with nonlinear coupling through the boundary given by $$ \left\{\begin{array}{rcll} \frac{\partial u}{\partial n} & = & f(x,u,v) & \mbox{on } \partial \Omega, \\ \frac{\partial v}{\partial n} & = & g(x,u,v), \end{array}\right. $$ under suitable assumptions on the nonlinear terms $f$ and $g$. For the proof we use a fixed-point argument and the key ingredient is a Liouville type theorem for a system of Laplace equations with nonlinear coupling through the boundary of power type in the half space.

Citation

Download Citation

Julián Fernández Bonder. Julio D. Rossi. "Existence for an elliptic system with nonlinear boundary conditions via fixed-point methods." Adv. Differential Equations 6 (1) 1 - 20, 2001.

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1223.35171
MathSciNet: MR1799678

Subjects:
Primary: 35J65
Secondary: 35D05 , 35J25 , 35J55

Rights: Copyright © 2001 Khayyam Publishing, Inc.

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.6 • No. 1 • 2001
Back to Top