Existence Of Solutions For Some Kinds Of Nonlinear Multi-point Boundary Value Problems

This thesis of master is composed of four chapters, which mainly study the nonlinear multi-point boundary value problems.In chapter two, by means of the fixed-point theorem, we discuss the existence of at least three positive solutions to the second-order nonlinear multi-point boundary value problems as follow:where f,g∈C([0,1]×[0,∞),[0,∞)),ξ_i,η_i∈(0,1),ξ_i＜ξ_i+1,η_i＜η_i+1,i=1,2,...,m-3,a_i≥0,b_i≥0,c_i≥0,d_i≥0,(i=1,2,...,m-2),and 0＜(?).Chapter three mainly considers three-point boundary value problems for even-order differential systemswhere 0＜ξ,η＜1,0＜α＜1/ξ,0＜β＜1/η, and f,g∈C([0,1]×[0,∞),[0,∞)).We form and analyse Green function, by means of the Leggett-Williams fixed-point theorem in cone in Banach space, we study and prove the existence of at least three positive solutions to the system.In the last chapter, we investigate the existence of at least a solution to the third-order nonlinear differential systems as follow:where f_i∈C([0,1]×R³,R),g_i∈C(R^m_3-i+2,R),h_i∈C(R^n_3-i+2,R),A_i,B_i,C_i∈R,ξ_iki,η_iji∈(0,1),k_i=1,2,…,m_i, j_i=1,2,…,n_i, i=1,2.We prove the existence of solution for the boundary value problem with the use of topological degree and lower and upper solution method.