带超越共振点非线性项的二阶常微分方程边值问题的可解性

Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points

考虑非线性二阶常微分方程边值问题:{u″+f(t,u)=h(t),t∈(0,1),u(0)=u(1)=0,得到了当f(t,s)/s在某些"较小的集合"上超出特征值区间[λ_(k0),λ_(k0+1)]时,该问题解的存在唯一性结果。

We study the existence and uniqueness of solutions of the boundary value problem for nonlinear second-order ordinary equations：{u″＋f（ t,u） = h（ t）,t∈（ 0,1）,u（ 0） = u（ 1） = 0,under the conditions that f（t,s）s may exceeds the eigenvalue interval [λk0,λk0＋1]in some＂smaller sets＂. The existence and uniqueness of solutions of this equation are obtained.