## Advances in Differential Equations

### 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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867434

Mathematical Reviews number (MathSciNet)
MR2331523

Zentralblatt MATH identifier
1154.35027

#### Citation

Sato, Jun-ichi. On the existence and nonexistence of solutions for an elliptic system in unbounded domains. Adv. Differential Equations 12 (2007), no. 7, 759--780.https://projecteuclid.org/euclid.ade/1355867434