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.