About Lane - Emden Hamiltonian In The Form Of Existence And Multiplicity Of Solutions Of The Systems Is Studied

Along with science’s and technology’s development,the nonlinear functional anal-ysis has aroused people’s widespread interest day by day. It is not only an important branch of math, but also the scientific explanation of the various phenomena for the physical, chemical, biological as well as different subjects. The existence and multi-plicity of solutions for Hamiltonian system are also the hot spots which have been discussed in recent years.In this paper, under the more general superlinear conditions, we make use of (Symmetric) Mountain Pass Lemma, Fountain Theorem, Ricceri’s variational principle and refined Bolle’s method to study the existence and multiplicity of solutions for several kinds of Hamiltonian system.The thesis is divided into two chapters according to contents.In chapter1, under much weaker superlinear assumptions, we study the existence of infinitely many solutions for homogeneous and non-homogeneous Hamiltonian sys-tem by (Symmetric) Mountain Pass Lemma, Fountain Theorem as well as the refined Bolle’s method and where p>1and Ω is a smooth bounded domain in RN. Our results generalize many recent studies.In chapter2, by using the Ricceri’s variational principle and (Symmetric) Moun-tain Pass Lemma, we consider the existence of nonlinear solutions for a class of Hamil-tonian system of Lane-Emden type involving positive parameter where p>1, parameter λ∈R1and is a bounded smooth domain in RN. Our resultsgeneralize some known studies.