共振条件下一类三阶m-点边值问题解的存在性

Existence of Solution for Third Order m-point Boundary Value Problems at Resonance

考虑共振情形下三阶微分方程m-点边值问题x'''(t)=f(t,x(t),x'(t),x"(t))+p(t),t∈(0,1), x(0)=0,x"(0)=0,x'(1)=sum from i=1 to m-1 a_ix'(ξi),其中a_i≥0,0<ξ1<ξ2<…<ξm-2<1且Σ_(i=1)^(m-2) a_i=1.利用Mawhin重合度拓展定理,得到该问题解存在性的新的结果.

In this paper, we consider a third order m-point boundary value problem：x＇＇＇（t）=f（t,x（t）,x＇（t）,x＂（t））＋p（t）,t∈（0,1）, x（0）=0,x＂（0）=0,x＇（0）=0,x＇（1）=∑i=1^m-2 aix＇（ξi）,where ai≥0,0〈ξ1〈ξ2〈…〈ξm-2〈1. Under the resonance condition ∑i=1^m-2 ai=1, by means of Mawhin＇s continuation theorem, a new result on the existence of solutions is obtained.