一类分数阶脉冲微分方程Dirichlet边值问题非平凡解的存在性  

The Existence of Nontrivial Solutions for an Impulsive Fractional Differential Equation with Dirichlet Boundary Conditions

作　　者：许亮 李培峦[1] XU Liang;LI Fei-luan(School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023,China)

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《数学的实践与认识》2020年第2期235-242,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11301153,61673008);中国博士后基金(2017M612392).

摘　　要：研究了一类带有脉冲的分数阶微分方程Dirichlet边值问题非平凡解的存在性.通过利用变分法和Morse理论证明了此分数阶脉冲微分方程至少存在一个非平凡解.In this paper,we studied the existence of nontrivial solutions for an impulsive fractional differential equation with Dirichlet boundary conditions.By using variational methods and Morse theory,we proved that the impulsive fractional differential equations have at least one nontrivial solution.

关 键 词：MORSE理论 脉冲 分数阶微分方程 变分法 非平凡解 

分 类 号：O175.8[理学—数学]