Abstract
We are concerned with the nonlinear parabolic system
Delta u - au - partial derivative u/partial derivative t = lambda p(x, t) f (v),
Delta u - bu - partial derivative v/partial derivative t = mu q(x, t)g (u),
in R-+(n) x (0, infinity), subject to some Dirichlet boundary conditions, where the potentials p, q, a and b are allowed to satisfy some hypotheses related to the parabolic Kato class P-infinity (R-+(n)), the functions f and g are nonnegative nondecreasing and continuous. More precisely, we shall prove the existence of positive continuous solutions with precise global behaviour. We will use some potential theory arguments.