Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 143, pp. 1-8.

Title: Existence of positive solutions for some
nonlinear parabolic equations in the half space

Author: Abdeljabbar Ghanmi (Campus Univ., Tunis, Tunisia)

Abstract:
 We prove the existence  of positive  solutions to the
 nonlinear parabolic equation
 $$
 \Delta u - \frac{\partial u}{\partial t}=p(x,t)f(u)
 $$
 in the half space $\mathbb{R}^n_{+}$, $n\geq 2$, 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.

Submitted June 18, 2010. Published October 12, 2010.
Math Subject Classifications: 35J55, 35J60, 35J65.
Key Words: Parabolic Kato class; parabolic equation; positive solutions.