Abstract
We show that positive continuous solutions exist for the nonlinear 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) on R-n x (0, infinity), n >= 3 with boundary conditions u(x, 0) = phi(x), v(x, 0) = psi(x) for nonnegative constants lambda and mu, provided that the functions f, g are nonnegative continuous and nondecreasing on (0, infinity). Also the potentials p, q are nonnegative and are required to satisfy some hypotheses related to the parabolic Kato class P-infinity(R-n). (C) 2009 Elsevier Ltd. All rights reserved.