Abstract
We prove some existence results of positive continuous solutions to the semilinear parabolic system Delta u - partial derivative u/partial derivative t = lambda p(x, t)g(v), Delta v - partial derivative v/partial derivative t = mu q(x, t)f(u) in an unbounded domain D with compact boundary subject to some Dirichlet conditions, where lambda and mu are nonnegative parameters. The functions f, g are nonnegative continuous monotone on (0, infinity) and the potentials p, q are nonnegative and satisfy some hypotheses related to the parabolic Kato class J(infinity)(D). (C) 2010 Elsevier Inc. All rights reserved.