Positive Solution Of Higher-Order Nonlinear Boundary Value Problems For Ordinary Differential Equations

In this paper,we study the higher order boundary value problem by using the knowledge of nonlinear functional analysis. This thesis includes the following three contents.Chapter 1 We study the positive solution of a singular third-order three-piont boundary value problems with parameters .By means of the fixed point theorems on cones and vector field analysis,we obtain one positive solution and multiple positive solutions.Chapter 2 We study the four order boundary value problem,including positive solution for a class of singular fourth-order nonlinear eigenvalue problems .g(t)∈C((0,1),[0,+∞)),f(u,v)∈C([0,+∞)×(-∞,0),[0,+∞)), a≥0, b≥0, c≥0, d≥0 andΔ= ac + ad + bc> 0,here g(t) is allowed to be singular at t = 0, t = 1.By means of the fixed point theorems on cones,we obtain one positive solution and multiple positive solutions.Chapter 3 We study the hight order boundary value problem,the order is 2n. is considered,here a(t) is allowed to be singular at t=0,t=1,f(t,v₁,v₂,…,v_n) is allowed to be singular at v_i = 0(i = 1,2,…n).We can obtain existence of two positive solutions by Guo-KrasnoseVskii's fixed point theorem ,at the condition M∫₀¹ k_n-1(s,s)a(s)ds < (?).