Periodic Solutions For Two Classes Of Variable Coefficient Wave Equations

In this thesis,we prove the existence of the periodic equations of the variable coeffi-cient nonlinear wave equation and the variable coefficient Kirchhoff type wave equation by using the Nash-Moser iterative method and the Lyapunov-Schmidt reduction technique.This thesis contains four chapters:In the first chapter,we introduce the background,research methods and related results on periodic solutions for wave equations.Then introduce the physical background of Kirchhoff equations,several common equations of Kirchhoff type,related results and research status of Kirchhoff equations.Finally,introduce the main contents and the scientific significance of this thesis.In the second chapter,we prove the existence and regularity of periodic solutions for variable coefficient wave equation with Dirichlet-Neumann boundary conditions via Lyapunov-Schmidt reduction and Nash-Moser iteration.In the third chapter,we prove the existence,regularity and local uniqueness of peri-odic solutions for the Kirchhoff type equation p(x)utt-(g(x)ux)x(1+?0?q(x)ux2dx)=?g(x,t),x ?(0,?),t?R,(0.0.1)by the Nash-Moser iterative method and we prove the solution depend smoothly on the parameters by the Whitney extension technique.In the fourth chapter,we prove the existence,regularity and local uniqueness of periodic solutions for Kirchhoff type equation(0.0.1)with periodic boundary conditions.The proof relies on Lyapunov-Schmidt reduction and Nash-Moser theorem.