Existence of a periodic solution for some nonlinear partial differential equations using fixed point theory in banach spaces

The aim of this thesis is to study the existence of a periodic solution for nonlinear partial differential equations using fixed point theory in Banach space. In Section 1, we introduce important preliminaries and background of partial differential equations and functional analysis. In Section 2, we investigate the existence solution of the ChafeeInfante equation with time periodic initial condition. Using the topological degree theorem, we establish the existence of a limit point to an auxiliary problem, which is the non-trivial time periodic weak solution of the considered problem. In Section 3, we investigate the existence solution of a p-Laplacian Chafee-Infante equation with time periodic initial condition. Using the topological degree theorem, we establish the existence of a limit point to an auxiliary problem, which is the non-trivial time periodic weak solution of the considered problem. Keywords: Periodic solution, Neumann boundary, Degenerate parabolic equation