Lower and upper solutions for the heat equation on a polygonal domain of R2

Abstract : We consider the nonlinear periodic-Dirichlet heat equation on a polygonal domain of the plane in weighted Lp-Sobolev spaces equation presented Here f is Lp(0; T;Lpμ(Ω)-Caratheodory, where L pμ(Ω) = {v ε Lploc(Ω) : rμv ε Lp(Ω)}, 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 first give existence results in an abstract setting obtained using degree theory. We secondly apply them for polygonal domains of the plane under geometrical constraints.