Abdi Tadesse (PhD)Sahile Tesfaye2018-07-192023-11-042018-07-192023-11-042016-07http://etd.aau.edu.et/handle/123456789/9303The purpose of this paper is to prove the existence of a solution in the presence of lower and upper solutions for the nonlinear periodic-Dirichlet heat equation on a polygonal domain Ω of the plane in weighted Lp-Sobolev spaces. Consider the problem; ∂tu − Δu = f(x, t, u), in Ω × (−π, π), u = 0, on ∂Ω × (−π, π), u(•,−π) = u(•, π) in Ω, loc (Ω)}, with a real parameter μ and r(x) the distance from x to the set of corners of Ω. 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 constraintsenMethod of Lower and Upper SolutionsThesis