Study On The Existence Of Solution On Nonlinear Differential Equations Via Variational Method

Nonlinear differential equations are widely used in today's scientific research and have extensive applications of mechanics,physics,astronomy,biology,medicine,economics and other scientific fields.Author mainly studies the existence of solutions on two kinds of nonlinear differential problems via variational method.Specially speaking,applying the minimization principle and the mountain lemma as well as the Nehari manifold method,a class of fourth-order differential boundary value problems and a class of fractional Schr?dinger-Poisson problems are studied respectively,and some existence of ground state solutions are obtained,which generalizes the corresponding results in recent some literature.This paper mainly studies the existence of the ground state solutions of the two problems: a class of fourth-order differential problem and a class of fractional Schr?dinger Poisson problem.This article is organized as follows:In the first chapter,the author mainly introduces the background of the above two types of equations and the significance of the research of these two types of equations,and gives the relevant definitions and lemmas.In the second chapter,the author applies the minimization principle and the mountain lemma to study the existence of the fourth-order differential equation,and gives a detailed proof of the obtained results.In the third chapter,the author gives a detailed argument about the results obtained by establishing a global compact lemma and combing the extreme values of Nehari manifold.In the fourth chapter,the author mainly introduces the brief summary and outlook for this paper.