Solvability Of Some Classes Of Boundary Value Problems Of Ordinary Differential Equations

In this paper,by using the generalized Green’s function,the fixed point theorem of cones and the Leray-Schander homotopy continuation method,we study the solvability of some classes of boundary value problems of ordinary differential equations.The main works are:1.The solvability of the following linear second-order periodic boundary value prob-lem The method is based upon defining and constructing the generalized Green’s func-tion of linear second-order periodic boundary value problems,where λ=4k2Ï€2,k= 1,2,3,…,f:[0,1]â†'R is continuous.2.By using the generalized Green’s function of Sturm-Liouville problems,we study the solvability of the following linear fourth-order boundary value problem where β=2k2Ï€2,(α/(kÏ€)4+β/(kÏ€)2=1,k=1,2,3,…,f:[0,1]â†'R is continuous.3.The existence of positive solutions of the following nonlinear fourth-order boundary value problem The method is based upon the fixed point theorem of cone extension or compression,where continuous.4. The solvability of the following nonlinear second-order periodic boundary value problemThe proof of our results is based on the Leray-Schauder homotopy continuation method and the Landesman-Lazer condition, where f∈L2(0,1), g:Râ†'R is continuous.