Affine-periodic Solutions For Higher Order Ordinary Differential Equations

This dissertation mainly studies the existence of affine-periodic solutions to higher order ordinary differential equations.Affine-periodic solutions is a new mathematical topic in dynamical system,and it is of great significance from the perspective of pure mathematics.In addition,from the point of practical applications,it plays an important role in the dynamics of rigid bodies,dynamics of typhoon,spiral wave,Bloch wave and so on and so forth.This dissertation is divided into five chapters.The first chapter includes some history and background of affine-periodic solutions,and some problems of solving equations.The second chapter introduces and proves a kind of monotone iterative technique for solving nonlinear operator equation.The third chapter obtains a type of maximum principle for higher order ordinary differential operator with respect to affine-periodic boundary conditions.This is the main innovation of this dissertation.The fourth chapter applies the maximum principle in the third chapter and the monotone iterative technique in the second chapter to the existence problem of affine-periodic solutions for higher order ordinary differential equations.The fifth chapter gives a summary and outlook for this dissertation.The end of this dissertation includes some references,a brief introduction of the author,some papers of the author published,and thanks.