一类二阶微分方程三点边值问题多解的存在性

Multiple Positive Solutions of Second Order Differential Equations with Three Point Boundary Value Problems

文章利用不动点指数理论,在Banach空间中讨论了方程-u″=f(t,u(t))u(0)=θu(1)=cu(ξ).其中:c>0,ξ>0,且0<cξ<1,得到了这类边值问题正解存在的充分条件,推广和改进了相关文献的结论。

The existence of multiple positive solutions of the second order three-point boundary value problem {-u=f（t,u（t）） u（0）=θ u（1）=cu（ξ） on Banach space is discussed. We show the exsistence of multiple positive solutions by applying the fixed index method. The results of the literature are developed and extended.