Existence of positive solutions for some nonlinear parabolic equations in the half space - Abdeljabbar Ghanmi (Electronic Journal of Differential Equations, 2010)
We prove the existence of positive solutions to the nonlinear parabolic equation $$ Delta u - fracpartial upartial t=p(x,t)f(u) $$ in the half space $mathbbR^n_{+}$, $ngeq 2$, 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.