三阶时滞微分方程边值问题正解的存在性

运用锥上的不动点定理, 研究三阶时滞微分方程边值问题{u(t)+λa(t)f(t,u(t-τ))=0, t∈(0,1), τ>0,u(t)=0,-τ≤t≤0,u(0)=u″(0)=0,u(1)=αu(η)正解的存在性, 其中 λ 是参数, 且 0<η<1, 0<α<1/η, f:［0,1］×［0,∞］→［0,∞)连续。

Existence of positive solutions for boundary value problems of third-order delay differential equations

By applying the fixed point theorem on the cone, this paper studies the existence of positive solutions for boundary value problems of third-order delay differential equation{u(t)+λa(t)f(t,u(t-τ))=0, t∈(0,1),τ>0,u(t)=0,-τ≤t≤0,u(0)=u″(0)=0,u(1)=αu(η)where λ is parameter, and 0<η<1, 0<α<1/η, f:［0,1］×［0,∞］→［0,∞) is continuous.