Study On The Periodic Solutions Of A Class Of 2nth Order Nonlinear Duffing Equations With Damping

The nonlinear differential equation is paid closed attention because they relate wild field. The existence and uniqueness of the periodic solution of these problems are always one of the central issue of the research, there are many methods to study it, such as algebraic method, variational method, fixed point method, topological degree homotopy method, monotone iterated method, hemeomorphism method.This paper first discussa kind of differential equations of 2nth order with damping in Banach spaces, using Leray-Schauder degree theorem.Then try to discuss the uniqueness of periodic solutionunder (L₀) condition. Thirdly, by virtue of homeomorphism extension and fixedpoint method, we discuss the existence of periodic solution of 2nth order differential equation.