非线性两点边值问题的存在唯一性

Existence Uniqueness for the Nonlinear Two-point Boundary Value Problems

对于非线性两点边值问题x″=f(t,x,x′), x(0)=A, x(1)=B,我们在f,fx,fx′,β(t),α′(t)都连续,且fx≥-β(t), -α(t)≤fx′≤M(1+|x′|),max β(t)-α2(t)+2α′(t)4t∈[0,1] ≤λ2<π24,α(1)≤2λcotλ,这些条件之下证明解之存在且唯一.

In this paper, we study the nonlinear two-point boundary value problems x″=f(t,x,x′), x(0)=A, x(1)=B, We proved existence-uniqueness for the solution under the conditions that f,f_x,f_(x′),β(t),α′(t) are all continuous and f_x≥-β(t), -α(t)≤f_(x′)≤M(1+|x′|),maxβ(t)-α~2(t)+2α′(t)4t∈[0,1]≤λ~2<π~24,α(1)≤2λcotλ.