微分方程-u″=λ^2u＋αf（u）＋g（｜u＇｜）边值问题正解的存在唯一性

Unique existence of positive solution of boundary value problem for a differential equation -u″=λ+2u+αf(u)+g(|u′|)

考虑如下边值问题-u″=λ2u+αf(u)+g(u′),u(0)=u(1)=0正解的存在唯一性.证明了在满足一定条件下,对任一0<λ<π,α≥0的边值问题存在唯一正解.

Considering the boundary value problem -u″=λ^2u＋αf（u）＋g（｜u＇｜）,u（0）=u（1）=0, we proved that under certain assumptions, for all 0 〈λ, 〈π, α≥ 0 the boundary value problem ex- ists unique positive solution.