测度链上非线性微分方程的三正解

摘要

运用文[1]中的Leggett-Williams不动点定理,我们给出了测度链上的非线性微分方程-x△△(t)=f(t,x(σ(t))),t∈[a,b]关于两点边值条件αx(a)-βx△(a)=0,γx(σ(b))+δx△(σ(b))=0三正解存在性准则.%Criteria are developed for the existence of three positive solutions for the nonlinear differential equation - x△△ (t) = f ( t, x (a (t) ) ), t∈ [ a, b] with general two points boundary conditions αx(a) -βx△(a) = 0, γx(a(b) ) +δx△ (σ(b) ) = 0 on a measure chain by using LeggettWilliams fixed point theorem[1].