测度链上非线性微分方程的特征值问题

Eigenvalue problem for a nonlinear differential equation on a measure chain

讨论了非线性特征值问题 u△△(t) +λa(t)f(u(δ(t) ) ) =0 ,t∈ [0 ,1]u(0 ) =0 =u(δ(1) ) 正解的存在性 .这里 [0 ,1]是一可测链 ,a与f取正值 ,且limx→ 0 +f(x)x 与limx→∞f(x)x

The existence of positive solution for nonlinear eigenvalue problems u △△ (t)+λa(t)f(u(δ(t)))=0,t∈ u(0)=0=u(δ(1))is discussed.Where closed interval 1] is a measure chain, a and f are positive value functions, is a measure chain, a and f are positive value functions, lim x→0 +f(x)x and lim x→∞f(x)x uncertainly exist.