Existence and asymptotic behaviour of positive solutions for semilinear elliptic systems in the Euclidean plane

Abstract

We study the semilinear elliptic system $$ Delta u=lambda p(x)f(v),Delta v=lambda q(x)g(u), $$ in an unbounded domain D in $ mathbb{R}^2$ with compact boundary subject to some Dirichlet conditions. We give existence results according to the monotonicity of the nonnegative continuous functions f and g. The potentials p and q are nonnegative and required to satisfy some hypotheses related on a Kato class.

Keywords

• Green function
• semilinear elliptic systems
• positive solution