%0 Journal Article
%T 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<br>Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points
%A 王素云
%A 李永军&lt
%A br&gt
%A WANG Su-yun
%A LI Yong-jun
%J 山东大学学报（理学版）
%D 2018
%R 10.6040/j.issn.1671-9352.0.2017.647
%X 摘要： 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［λk0, λk0+1］ 时,该问题解的存在唯一性结果。<br>Abstract: 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
%K 二阶常微分方程边值问题
%K 解的存在唯一性
%K 特征值
%K 压缩映象定理
%K &lt
%K br&gt
%K second-order boundary value problem
%K eigenvalue
%K existence and uniqueness of solutions
%K contraction mapping principle
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2017.647