摘要
利用一类分数阶微分方程边值问题的变分法,建立了该边值问题解存在的充分条件.然后将问题归结为一个等价的积分形式,使得边值问题的解被定义为对应泛函的临界点.最后利用山路引理,建立了该边值问题解的存在性.
A sufficient condition for the existence of the solution of a boundary value problem for a class of fractional-order differential equations is established by using the variational method.Then the problem is reduced to an equivalent integral form so that the solution of the boundary value problem is defined as the critical point of the corresponding functional.Finally,the existence of the solution to the boundary value problem is established by using the mountain road lemma.
作者
黎文博
周文学
吴亚斌
张敏
LI Wenbo;ZHOU Wenxue;WU Yabin;ZHANG Min(College of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)
出处
《云南大学学报(自然科学版)》
CAS
CSCD
北大核心
2024年第2期201-212,共12页
Journal of Yunnan University(Natural Sciences Edition)
基金
国家自然科学基金(11961039)
兰州交通大学校青年科学基金(2017012)。
关键词
临界点理论
变分法
边值问题
梯度
critical point theory
variational method
boundary value problem
gradient