一个高阶边值问题

A Higher Order Boundary Value Problem

本文考虑如下高阶多点边值问题：ｘ（ｎ）＝ｆ（ｔ，ｘ，ｘ＇，…，ｘ（ｘ－１），ｘ（０）＝ｘ（ξ）＝（１）＝ｘ＇（ξ）＝…＝ｘ（ｎ－３）（ξ）＝０，其中ξ∈（０，１）．对于ｆ有非线性增长的情况，利用基于度理论的不动点定理，建立了某些存在唯一性定理．

In this paaper the following higher order multipoint boundary value problem: x(n)=f(t, x, x', ...,x(x-1) ),x(0) =x(ξ) =x(1) =x' (ξ) = ... =x(x-3) (ξ) = 0 is conidered for ξ∈ (0, 1). For the case that f has noalinear growth, some existence and uniqueness theoreme for above problem are established by using certain fixed point theorem based on the degree theory.