Multiplicity of solutions for impulsive differential equation on the half-line via variational methods

Boundary value problems

Jianli Li¹  Huiwen Chen²  Zhimin He³ 

[1] School of Mathematics and Physics, University of South China, Hengyang, People’School of Mathematics and Statistics, Central South University, Changsha, People’s Republic of China

关键词: impulsive differential equation;    variational methods;    critical points;    half-line;    34B08;    34B15;    34B37;    58E30;   

DOI  :  10.1186/s13661-016-0524-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the existence of solutions for a second-order impulsive differential equation with two parameters on the half-line is investigated. Applying variational methods, we give some new criteria to guarantee that the impulsive problem has at least one classical solution, three classical solutions and infinitely many classical solutions, respectively. Some recent results are extended and significantly improved. Two examples are presented to demonstrate the application of our main results.

【 授权许可】

CC BY