分数阶常微分方程多点边值问题的上下解方法

The lower and upper solution method of fractional-order multiple-point differential equation boundary value problem

摘要:

本文应用上下解方法研究了分数阶常微分方程多点边值问题 x^(δ)(t),=f(t,x(t)),t∈[a,b],a>0, x(a)+∑{k=1}^{m}a_{k}x(t_{k})=c 解的存在性.其中f:[a,b]×R→R是L^(1)-Caratheodory函数,δ∈(0,1],c∈R,t_{k}(k=1,2,...,m)为满足a0的常数.

Abstract:

In this paper,by applying upper and lower solution method,we study the existence of solution of fractional-order multiple-point boundary value problem x^(δ)(t),=f(t,x(t)),t∈[a,b],a>0, x(a)+∑{k=1}^{m}a_{k}x(t_{k})=c where f:[a,b]×R→R is L^(1)-Caratheodory function,δ∈(0,1],c∈R,t_{k}(k=1,2,...,m) are constants and satisfying a0.