We consider the nonlinear periodic-Dirichlet heat equation on a polygonal domain ? of the plane in weighted Lp-Sobolev spaces ?tu -?u = f(x,t,u); in ?x (-π; π);u = 0; on ?? (-π, π),u(?,-π) = u(?, π) in ? Here f is Lp(0; T;Lpu(?))-Carathéodory, where Lpu(?) = {με Lp/ loc(?):r~uμ ε Lp(?)} with a real parameter μ and r(x) the distance from x to the set of corners of. We prove some existence results of this problem in presence of lower and upper solutions well-ordered or not. We rst give existence results in an abstract setting obtained using degree theory. We secondly apply them for polygonal domains of the plane under geometrical constraints.
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