Existence Of Solutions For High-Order Nonlinear Boundary Value Problems

In this paper, we firstly construct generalized Green's function of n-order local boundary value problem and non-local boundary value problem Then we obtain the existence results on fourth-order boundary value problems by using Leray-Shauder theorem. Furthermore, we establish the existence of positive solutions of n-order local and non-local boundary value problems by fixed point theorem. Finally, we give some examples to verify our results.