Abstract
We prove the existence of positive solutions to the nonlinear parabolic equation
Delta u -partial derivative u/partial derivative t = p(x, t)f(u)
in the half space R-+(n), n >= 2, subject to Dirichlet boundary conditions. The function f is nonnegative continuous non-increasing, and the potential p is nonnegative and satisfies some hypotheses related to the parabolic Kato class. We use potential theory arguments to prove our main result.