测度链上非线性微分方程的三正解(英文)

TRIPLE POSITIVE SOLUTIONS FOR A NONLINEAR DIFFERENTIAL EQUATION ON A MEASURE CHAIN

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-xΔΔ(t) =f(t,x(σ(t) ) ) ,t∈ [a,b]关于两点边值条件αx(a) - βxΔ(a) =0 ,γx(σ(b) ) +δxΔ(σ(b) )

Criteria are developed for the existence of three positive solutions for the nonlinear differential equation -x^(ΔΔ)(t)=f(t,x(σ(t))),t∈\ with general two points boundary conditions αx(a)-βx~Δ(a)=0,γx(σ(b))+δx~Δ(σ(b))=0 on a measure chain by using Leggett-Williams fixed point theorem\.