有序Banach空间中一类分数阶边值问题的正解  

Positive Solutions for Fractional Boundary Value Problems of a Class in Ordered Banach Spaces

作　　者：李小龙 LI Xiao-long(College of Mathematics and Statistics,Longdong University,Qingyang 745000,China)

机构地区：[1]陇东学院数学与统计学院

出　　处：《安徽师范大学学报（自然科学版）》2019年第6期515-519,共5页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(11561038,11661051);甘肃省自然科学基金项目(18JR3RM238)

摘　　要：讨论了有序Banach空间E中分数阶微分方程边值问题:CD^α0+u(t)=f(t,u(t)),0≤t≤1,u(0)=u′(1)=u″(0)=θ正解的存在性,其中2<α≤3,CD^α0+为Caputo分数阶微分,f:[0,1]×P→P连续,P为E中的正元锥。通过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边值问题正解的存在性结果。The existence of positive solutions for the boundary value problem of a class of the fractional differential equation CD^α0u(t)=f(t,u(t)),0 ≤ t ≤ 1,u(0)=u′(1)=u″(0)=θin an ordered Banach spaces E was discussed,where2<α≤3,andCD^α0is the Caputo fractional differentiation,f:[0,1]×P→P is continuous,and P is 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.

关 键 词：分数阶边值问题 正解 凝聚映射 不动点指数 

分 类 号：O175.15[理学—数学]