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

The boundary value problem for differential equation is an important branch in the study of differential equation theory,it has a broad application background and important theoretical guidance in physics, astronomy,biology, sociology and so on. Therefore,the existence and multiplicity of solutions become one of important research topic in the fields of applications. As we all know, it is quite difficult to find out the solutions of the differential equation. So the theoretical study of the existence of the solutions and their characters from the theory attract a great attention. With solving these problems, most methods are applied.In this paper, by using global bifurcation theory, we get the existence of nodal solutions for several kinds of differential equation boundary value problem. The dissertation contains three chapters.In chapter1, we consider an second-order semipositone integral boundary value problem: whereλ> Ois a parameter,f∈C(R,R),a∈L[0,1] is nonnegative with0<∫01a2(s)ds<l.we get that the boundary value problem has at least2i nodal solu-tions when f satisfies certain conditions by using global bifurcation theory. In chapter2, we consider an sixth-order m-point boundary value problem: where f:R×R×R→R is a given sign-changing continuous function, m≥3,ηi∈(0,1)and αi>0for i=1,2,…,m-2with we get the existence of multiplicity nodal solutions by using Rabinowitz’s global bifurcation theory from Oand∞.In chapter3, we consider an p-Laplacian problem with sign-changing weight: where r=|x|,x∈B,B is an unit ball of RN,m(r) is a sign-changing function, φp(s)=|s|P-2s,f:R→R is continuous. we get the existence of multiplicity nodal solutions.