EXISTENCE AND ASYMPTOTIC BEHAVIOUR OF POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS IN THE EUCLIDEAN PLANE

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 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.