高阶微分方程(n-1,1)型多点边值问题的解

Solutions of (n-1,1) type multi-point boundary value problems for higher-order differential equations

研究高阶微分方程x(n)(t)=f(t,x(t),x′(t),,x(n-1)(t)),0<t<1满足边值条件1(1)m i(i)ixαxξ==∑,x(i)(0)=0(i=0,1,…,n-2)或(2)(2)1n(1)mi n(i)i(0)0ixαxξx==∑,=(i=0,1,…,n-2)解的存在性,其中,αi∈R(i=1,,m),n≥2是整数,且0<ξ1<<ξm<1,f连续,并分别获得了这些问题存在解的充分条件.与传统结果相比,本文定理中的非线性项可以依赖于所有的低阶导数.

Given the higher-order differential equation x^（n）（t）=,（t,x（t）,x＇（t）,…,x^（n-1）（t））,0〈t〈1 being subjected to one of the following multi-point boundary value conditions x（1）=∑i=1^ma jx（ξi）,x^（i）（0）=0（i=0,1,…,n-2）and x^（n-2）（1）=∑i=1^naix^（n-2）（ξi）,x^（i）（0）=0（i-0,1,…,n-2 , sufficient conditions for the existence of at least one solution at resonance would be established, It is emphasized thatfdepends on all lower-order derivatives.