一类无穷区间上分数阶非局部边值问题正解的存在性

Existence of Positive Solutions for Nonlocal Boundary Value Problems of Fractional Order in Infinite Intervals

研究了一类无穷区间上非线性项含有导数项的分数阶微分方程非局部边值问题{D_0~α+u(t)+f(t,u(t),D_(0+)^(α-1)u(t))=0,t∈[0,∞)I_0^(2-α)u(t)︱t=0=0,lim t→∞D_(0+)^(α-1)u(t)=∑_(i=1)^(m-2)β_iD_(0+)^(α-1)u(ξ_i)正解的存在性.根据G(t,s)的相关性质及假设条件,运用Schauder不动点定理,证明了该边值问题至少有一个正解.

We study the existence of a positive solution of non-local boundary value problem in a class of non-linear terms of fractional order in infinite interval:{D_0~α+u(t)+f(t,u(t),D_(0+)^(α-1)u(t))=0,t∈[0,∞)I_0^(2-α)u(t)︱t=0=0,lim t→∞D_(0+)^(α-1)u(t)=∑_(i=1)^(m-2)β_iD_(0+)^(α-1)u(ξ_i)According to G(t,s)related properties and conditions,using Schauder fixed point theorem,we find that the boundary value problem has at least one positive solution.