The Study Of Periodic Solutions Of A Kind Of Subquadratic Hamiltonian Systems

The existence and multiplicity of periodic solutions of a kind of subquadraticHamiltonian systems are studied in our article. Firstly, to the study of existence prob-lem, we transform the problem of finding the solution(s) of Hamiltonian systems tothat of finding the critical point(s) of a suitable functional via variational principle,and then by the minimax methods, we can prove that the functional has at least onecritical point(or critical value), which is also the weak periodic solutions of nonlinearHamiltonian systems. Forward, the continuation of solutions imply that the weak solu-tions are also classic solutions of nonlinear Hamiltonian systems. Secondly, to the studyof multiplicity problem, we similarly transform the problem of finding the solutions ofsymmetric Hamiltonian systems to that of finding the critical points of a suitable evenfunctional via variational principle, and then by Z2index theory, we find at least2npairs of critical points of the functional, then we get at least2n pairs of periodic solutionsof a kind of subquadratic Hamiltonian systems that satisfy symmetrical condition.