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

被引:0
作者
Heidarkhani, Shapour [1 ]
Ferrara, Massimiliano [2 ]
Salari, Amjad [1 ]
Caristi, Giuseppe [3 ]
机构
[1] Razi Univ, Fac Sci, Dept Math, Kermanshah 67149, Iran
[2] Univ Mediterranea Reggio Calabria, Dept Law & Econ, Via dei Bianchi 2, Reggio Di Calabria 89131, Italy
[3] Univ Messina, Dept Econ, Via dei Verdi 75, Messina, Italy
来源
BOUNDARY VALUE PROBLEMS | 2016年
关键词
multiple solutions; perturbed impulsive differential equation; critical point theory; variational methods; BOUNDARY-VALUE-PROBLEMS; VARIATIONAL APPROACH; EXISTENCE; SYSTEMS;
D O I
10.1186/s13661-016-0581-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
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.
引用
收藏
页数:16
相关论文
共 52 条
[1]   Variational Approach to Fourth-Order Impulsive Differential Equations with Two Control Parameters [J].
Afrouzi, Ghasem A. ;
Hadjian, Armin ;
Radulescu, Vicentiu D. .
RESULTS IN MATHEMATICS, 2014, 65 (3-4) :371-384
[2]   Variational analysis for Dirichlet impulsive differential equations with oscillatory nonlinearity [J].
Afrouzi, Ghasem A. ;
Hadjian, Armin ;
Radulescu, Vicentiu D. .
PORTUGALIAE MATHEMATICA, 2013, 70 (03) :225-242
[3]  
[Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892
[4]  
[Anonymous], 1989, Series in Modern Applied Mathematics
[5]  
[Anonymous], 2008, CONT MATH APPL
[6]  
[Anonymous], 1997, Dynamic Impulse Systems: Theory and Applications
[7]  
[Anonymous], 1985, NONLINEAR FUNCTIONAL
[8]   An application of variational method to a class of Dirichlet boundary value problems with impulsive effects [J].
Bai, Liang ;
Dai, Binxiang .
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2011, 348 (09) :2607-2624
[9]  
Bainov D, 1989, Systems With Impulse Effect: Stability, Theory and Applications
[10]  
Benchohra M., 2006, Impulsive Differential equations and Inclusions