Electron. J. Diff. Equ., Vol. 2010(2010), No. 143, pp. 1-8.

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

Abdeljabbar Ghanmi

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.

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Abdeljabbar Ghanmi
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: Abdeljabbar.ghanmi@lamsin.rnu.tn

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