Advances in Differential Equations
- Adv. Differential Equations
- Volume 12, Number 7 (2007), 759-780.
On the existence and nonexistence of solutions for an elliptic system in unbounded domains
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.
Adv. Differential Equations Volume 12, Number 7 (2007), 759-780.
First available in Project Euclid: 18 December 2012
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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