有序Banach空间分数阶Robin边值问题的正解

Positive Solutions for Fractional Robin Boundary Value Problems in Ordered Banach Spaces

讨论了有序Banach空间E中Riemann-Liouville分数阶Robin边值问题:-Dα0+u(t)=f(t,u(t)),0≤t≤1,u(0)=u′(1)=θ正解的存在性,其中1<α≤2,f:[0,1]×P→P连续,P为E中的正元锥.利用非紧性测度的估计技巧及凝聚映射的不动点指数理论获得了该边值问题正解的存在性结果.

The existence of positive solutions for the Riemann-Liouville fractional Robin boundary value problem -D α 0 + u(t)=f(t,u(t)), 0≤t≤1,u(0)=u′(1)=θ in an ordered Banach spaces E is discussed, where 1<α≤2,f:[0,1]×P→P is continuous, and P is the cone of positive elements in E .An existence result of positive solutions is obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.