Existence of Positive Solutions for Some Nonlinear Parabolic Equations in the Half Space
نویسنده
چکیده
We prove the existence of positive solutions to the nonlinear parabolic equation ∆u− ∂u ∂t = p(x, t)f(u) in the half space R+, 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.
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تاریخ انتشار 2010