Cantor Families Of Periodic Solutions For Several Kinds Of Equations Via Nash-moser Iteration

In this thesis, we are mainly interested in Nash-Moser implicit function theo-rem, and apply Nash-Moser iterative technique to construct the periodic solutions of Kirchhoff equation with Neumann boundary conditions, the periodic solutions of wave equation with Sturm-Liouville boundary conditions, the periodic solutions of one-dimensional wave equation under Dirichlet and Neumann boundary conditions, the periodic solutions of one-dimensional Schrodinger equation under the general boundary conditions, respectively. This thesis contains five chapters.In Chapter1, we focus briefly on the background, research status, preparatory knowledge of the studied subject, our main works and the significance of the research in this Thesis.In Chapter2, we prove the existence, regularity and local uniqueness of the time-periodic solutions for Kirchhoff type equations subject to Neumann conditions.In Chapter3, the chapter is concerned with the existence of the time-periodic solutions for a class of wave equations utt-uxx=μf((?)t,x,u) with Sturm-Liouville boundary conditions. In Chapter4,we devote to the construction of the time-periodic solutions for one-dimensional nonlinear wave equations utt-uxx+mu=εg(x,(?)t,u) subject to both Dirichlet and Neumann boundary conditions for a large set of flrequen-cies.In Chapter5,we construct time-periodic solutions in several cases for one dimen-sional Schrodinger equation iut一uxx+V(x)uεf((?)t,x,u2)uunder the generalized Sturm-Liouville boundary conditions a1u(t,0)-b1ux(t,0)=0,a2u(t,π)+b2ux(t,π)=0, where a2/i+b2/i≠0,i=1,2.