### On the existence and nonexistence of solutions for an elliptic system in unbounded domains

Jun-ichi Sato

#### Abstract

In this paper, we study the existence and nonexistence of solutions for some systems of semilinear elliptic equations in an unbounded domain $\Omega$. The main objective of this paper is to discuss the relationship between the existence of solutions and the translation invariance of the domain $\Omega$. More precisely, we point out how the translation invariance of our domain plays a crucial role for the existence of our problem.

#### Article information

Source
Adv. Differential Equations, Volume 12, Number 7 (2007), 759-780.

Dates
First available in Project Euclid: 18 December 2012