Global Results Of Solutions For Several Kinds Of Boundary Value Problems Of Differential Equations

The nonlinear boundary value problem of differential equations is an important branch in the study of differential equation theory. All sorts of boundary value prob-lems of differential equation have resulted from mathematics, physics, cybernetics and so on. With solving these problems, many important methods and theories such as fixed point theory, topological degree method and bifurcation theory have developed gradually.This paper mainly investigates the existence and multiplicity of solutions for several kinds of boundary value problems of differential equation. The thesis con-tains three chapters.Chapter 1 considers an 2n-order m-point boundary value problem where f:R ×Rn→ R is continuous function, m≥ 3, ηi∈(0,1), αi> 0 andWe first give the spectral properties of the linearisation of boundary value problems (1). These spectral properties are then used to prove two global bifur- cation theorems. Finally, the existence of multiple solutions of (1) by using global bifurcation theorems is obtained.Chapter 2 discusses the complementary Lidstone boundary value problem where m≥1,F:RxRxR→R is a continuous function.It’s noted that the nonlinear term F involves y’. The derivative-depedent nonlinearities are seldom tackled. We obtain the existence of multiple solutions of (2) by using special techniques and the global bifurcation theorems.Chapter 3 investigates an second-order semipositone integral boundary value problem where λ> 0 is a parameter,f∈C(R, R), a∈L[0,1] is nonnegative with n<∫01a2(s)ds<1.Using global bifurcation theorems, we get the existence of multiplicity nodal solutions of (3) as well as the range of A under some conditions.