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[1]李小龙.Banach空间中分数阶微分方程Robin边值问题解的存在性[J].延边大学学报(自然科学版),2022,(02):95-99.
　LI Xiaolong.Existence of solutions for Robin boundary value problems of fractional differential equation in Banach spaces[J].Journal of Yanbian University,2022,(02):95-99.

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Banach空间中分数阶微分方程Robin边值问题解的存在性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 期数: 2022年02期页码: 95-99 栏目: 基础科学研究出版日期: 2022-07-20

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

文章编号:: 1004-4353(2022)02-0095-05

作者:: 李小龙; (陇东学院数学与统计学院, 甘肃庆阳 745000)

Author(s):: LI Xiaolong; (College of Mathematics and Statistics, Longdong University, Qingyang 745000, China)

关键词:: 分数阶边值问题; 不动点定理; 非紧性测度; 凝聚映射

Keywords:: fractional boundary value problem; fixed point theorem; noncompactness measure; condensing mapping

分类号:: O175.15

文献标志码:: A

摘要:: 讨论了Banach空间E中分数阶微分方程边值问题: -D^β_<sup>0⁺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^β_<sup>0⁺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.

Abstract:: The existence of solutions for the boundary value problem of a class of the fractional differential equation -D^β_0⁺u(t)=f(t,u(t)), 0≤t≤1, u(0)=u'(1)=θ in Banach spaces E is discussed, where 1<β≤2, D^β_0⁺ 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.

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备注/Memo

收稿日期: 2022-03-17
基金项目: 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)
作者简介: 李小龙(1976—),男,硕士,副教授,研究方向为抽象微分方程.

更新日期/Last Update: 2022-07-20