摘要
目的讨论一类含参数非线性分数阶微分方程多点积分边值问题解的存在性和唯一性。方法应用Banach空间中的不动点定理进行研究。结果与结论(1)E=C([0,T],R)为Banach空间,若存在非负函数g(t),使得■t∈[0,T],|f(t,u)|≤g(t),则边值问题在集合E中至少有一个解;(2)如果lim_(u→0)f(t,u)/u=0,则边值问题在集合E中至少有一个解;(3)若边值问题右端函数f(t,u)满足一定的条件,则边值问题有唯一解。
Purposes—To study the existence and uniqueness of solutions for multi-point integral boundary problems of Riemann-Liouville fractional differential equations with parameters.Methods—The fixed point principle in Bananch space is used for the proofs herein.Results and Conclusions—(1)For a Bananch space E=C([0,T],R),if there exists a nonnegative function g(t),■t∈[0,T],|f(t,u)|≤g(t),fractional differential equations has at least a solution in E.(2)If lim _(u→0) f(t,u)/u=0,fractional differential equations has at least a solution in E.(3)If f(t,u)satisfies some conditions,the solution of differential equations is unique.
作者
郑艳萍
李宣达
ZHENG Yan-ping;LI Xuan-da(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619,Shanxi,China;College of Sciences,Northeastern University,Shenyang 110819,Liaoning,China)
出处
《宝鸡文理学院学报（自然科学版）》
CAS
2023年第1期8-13,共6页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金
山西省应用基础研究计划项目(20210302124529)。
