Existence And Multiplicity Of Solutions To Boundary Value Problems For Nonlinear Fourth-order Differential Equations

In recent years,the boundary value problem of nonlinear differential equation is attracted by many experts in differential equation.In many fields,nonlinear differential equations are developing continuously.The study of these problems can be extended to theory,such as nonlinear analysis,biology,physics.And research findings can provide more theoretical basis in the field of space.So the nonlinear differential equation gives us important meaning and application value.In this paper,we mainly investigate the existence and multiplicity of three kinds of fourth-order with boundary value problem linear.In chapter 1,the background,significance,development history and present situation of the problems are introduced in this paper,as well as the definitions and theorems of symbols cited in this paper are briefly introduced.In chapter 2,a two-point boundary value problem for a class of coupled singular differential equations with parameters is discussed.In chapter 3,the two kinds of boundary value problems of fourth-order differential equations are discussed.For the first kind of boundary value problems of fourth-order differential equations we discuss by using a linear operator related to the first eigenvalue,the existence of positive solutions are the result.For the second boundary value problems of fourth-order differential equations we through the establishment of a concave functional,then we use Legget-Williams fixed point theorem for promotion.It is obtained that there are at least four positive solutions to the fourth order differential equation.we broaden the number of the original solution.In chapter 4,we summarized the paper and gives a brief outlook.