Existence And Multiplicity Of Homoclinic Solutions For Second Order Subquadratic Hamiltonian Systems

In this thesis, we mainly discuss the homoclinic solutions for second order subquadratic Hamiltonian systems, and obtain the existence and multiplicity of homoclinic solutions for this systems by variational methods.Chapter1is devoted to the evolution and development of variational methods, and the problems that will be studied.In Chapter2is devoted to some essential definitions and related preliminary theorems.In Chapter3, under some certain conditions, we introduce some theorem for this Hamilto-nian systems. Employing the mountain pass theorem and linking theorem, we get the nontrivial and multiple solutions of the problem.