Positive Solutions Of A Fourth-order Periodic Boundary Value Problem With Parameter

Boundary value problems(BVPs for short)of fourth-order ordinary differential equations have received much attention due to their striking applications to engineering,physics and so on.Recently,experts have found that BVP of fourth-order ordinary differential equation with periodic boundary condition has more important practical significance.And then,this kind of problem has become the focus of heated debate.In this paper,we consider the following periodic BVP(PBVP for short)of fourth-order differential equationwhere p?0,4a+16p~4<1,f?(C_[0,2?]×[0,+?),[0,+?)),?>0 is a parameter.In chapter 1,we introduce the research background and list some necessary preparatory knowledge which is needed in this thesis.In chapter 2,by using Guo-Krasnoselkii fixed point theorem,we discuss the existence of one or two positive solutions to the above PBVP.In chapter 3,by using Leggett-Williams fixed point theorem,we consider the multiplicity of solutions to the above PBVP.