Banach空间中分数阶微分方程Robin边值问题解的存在性  

Existence of solutions for Robin boundary value problems of fractional differential equation in Banach spaces

作　　者：李小龙 LI Xiaolong(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,甘肃庆阳745000

出　　处：《延边大学学报（自然科学版）》2022年第2期95-99,共5页Journal of Yanbian University（Natural Science Edition）

基　　金：甘肃省自然科学基金(21JR1RM337);甘肃省高等学校创新基金(2021B-270,2021B-262)。

摘　　要：讨论了Banach空间E中分数阶微分方程边值问题:-D_(0+)^(β)u(t)=f(t,u(t)),0≤t≤1,u(0)=u′(1)=θ解的存在性,其中1<β≤2,D_(0+)^(β)是标准的Riemann-Liouville分数阶导数,f:[0,1]×E→E连续.通过非紧性测度的估计技巧,在非线性项f满足较弱增长条件下利用凝聚映射的不动点定理获得了该边值问题解的存在性结果.The existence of solutions for the boundary value problem of a class of the fractional differential equation-D_(0+)^(β)u(t)=f(t,u(t)),0≤t≤1,u(0)=u′(1)=θin Banach spaces E is discussed,where 1<β≤2,D_(0+)^(β) is the standard Riemann-Liouville fractional derivative,f:[0,1]×E→E is continuous.The existence of the solution of the boundary value problem is obtained by using the fixed point theorem of condensed mapping under the condition of weak growth of nonlinear terms,by using the estimation technique of noncompactness measure.

关 键 词：分数阶边值问题 不动点定理 非紧性测度 凝聚映射 

分 类 号：O175.15[理学—数学]