Existence Of Period Solutions Of Dissipative Equation Under Superlinear Condition

Dissipative equation is an important model in physics.In this thesis,we study the existence and multiplicity of periodic solutions of superlinear Li(?)nard equation with forced term.Based on the Poincar(?)-Birkhoff twist theorem,we further consider the related problem of periodic solutions of superlinear second-order singular p-Laplace equation with forced term,and prove the existence and multiplicity of harmonic solutions and subharmonic solutions.The main structure of the thesis is as follows:In Chapter 1,we mainly introduce the background and development status of periodic solutions of dissipative equations,and briefly summarize the main research contents and characteristics.In Chapter 2,we study the existence of periodic solutions for superlinear Li(?)nard equation with forced term.Firstly,it is transformed into its equivalent Hamiltonian system by a transformation,and then the global existence and other related properties of solutions are proved.Finally,the proofs of Theorem 2.1 and Theorem 2.2 are completed by using Poincar(?)-Birkhoff twist theorem.In Chapter 3,by introducing three different types of isochronous systems,the difference and connection between the equations in Chapter 2 and Chapter 3 are explained.Then,we discuss the existence of solutions for superlinear second-order singular p-Laplace equation with forced term.Firstly,the auxiliary function is constructed such that the required function satisfies the local Lipschitz condition.Then,based on the method of studying Li(?)nard type equation in Chapter 2,the proofs of Theorem 3.1 and Theorem 3.2 are completed by using Poincar(?)-Birkhoff twist theorem and Arzela-Ascoli theorem.In Chapter 4,we summarize the main content of this thesis and think and prospect for further research.