有序Banach空间非线性Neumann边值问题正解的存在性

Existence of Positive Solutions for Nonlinear Neumann Boundary Value Problems in Ordered Banach Spaces

讨论了有序Banach空间E中的边值问题-u″(t)+Mu(t)=f(t,u(t)),0≤t≤1,u'(0)=u'(1)=θ的正解,其中f:[0,1]×P→P连续,P为E中的正元锥.通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果.

The existence of positive solutions for value problem- u″（ t） ＋ Mu（ t） = f（ t,u（ t））,0≤t≤1,u＇（ 0） = u＇（ 1） = θin an ordered Banach spaces E was discussed,where f： [0,1]× P→P was continuous,and P was the cone of positive elements in E. An existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.