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.
Citation
Jun-ichi Sato. "On the existence and nonexistence of solutions for an elliptic system in unbounded domains." Adv. Differential Equations 12 (7) 759 - 780, 2007. https://doi.org/10.57262/ade/1355867434
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