Multiple solutions for a class of perturbed second-order differential equations with impulses

Boundary value problems

Giuseppe Caristi¹  Massimiliano Ferrara²  Amjad Salari³  Shapour Heidarkhani³ 

[1] Department of Economics, University of Messina, Messina, Italy;Department of Law and Economics, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy;Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, Iran

关键词: multiple solutions;    perturbed impulsive differential equation;    critical point theory;    variational methods;   

DOI  :  10.1186/s13661-016-0581-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The present paper is an attempt to investigate the existence of weak solutions for perturbed impulsive problems containing a Lipschitz nonlinear term. The study bases itself on the most recent variational approaches to the smooth functionals which are defined on reflexive Banach spaces. The findings of the study, finally, revealed that, under appropriate conditions, such problems possess at least three weak solutions. According to the results, these solutions are generated by impulses when the Lipschitz nonlinear term is zero.

【 授权许可】

CC BY