一类二阶非线性四点边值问题正解的存在唯一性

Existence and uniqueness of positive solutions of a class of nonlinear second-order four-point boundary-value problem

运用单调迭代方法讨论二阶非线性常微分方程四点边值问题u″(t)+f(t,u(t))=0,t∈(0,1),u(0)=βu(ξ),u(1)=αu(η)正解的存在唯一性,其中ξ,η∈(0,1),0≤β(1-ξ)<1,0≤αη<1.推广和改进相关文献的结果.

By using the monotone iterative method,the existence and uniqueness of positive solutions of a nonlinear second-order four-point boundary-value problem u″（t）＋f（t,u（t））=0,t∈（0,1）,u（0）=βu（ξ）,u（1）=αu（η） were discussed,in the equation ξ,η∈（0,1）,0≤β（1-ξ）1,0≤αη1.As a result of this paper,the results of relevant literatures were generalized and improved.