Nontrivial solutions for discrete Kirchhoff-type problems with resonance via critical groups

被引:9
作者
Yang, Jinping [1 ]
Liu, Jinsheng [1 ]
机构
[1] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Shanxi, Peoples R China
关键词
discrete Kirchhoff-type problem; variational method; critical point; critical group; DIFFERENCE-SYSTEMS; EXISTENCE;
D O I
10.1186/1687-1847-2013-308
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we study the existence of nontrivial solutions for discrete Kirchhoff-type problems with resonance at both zero and infinity by using variational methods and the computations of critical groups.
引用
收藏
页数:14
相关论文
共 22 条
[1]  
[Anonymous], 1985, NONLINEAR FUNCTIONAL
[2]   Nontrivial periodic solutions for asymptotically linear resonant difference problem [J].
Bin, Hong-Hua ;
Yu, Han-She ;
Guo, Zhi-Ming .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 322 (01) :477-488
[3]  
Chang K.-C., 1993, INFIN DIMENS ANAL QU, DOI DOI 10.1007/978-1-4612-0385-8
[4]  
Kirchhoff G., 1883, MECHANIK
[5]   Existence of a positive solution to Kirchhoff type problems without compactness conditions [J].
Li, Yuhua ;
Li, Fuyi ;
Shi, Junping .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (07) :2285-2294
[6]  
Lions J.L., 1997, North-Holland Math. Stud., V30, P284
[7]   Nontrivial solutions for discrete boundary value problems with multiple resonance via computations of the critical groups [J].
Liu, Jinsheng ;
Wang, Shuli ;
Zhang, Jianming ;
Zhang, Fuwei .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (09) :3809-3820
[8]   Nontrivial solutions for resonant difference systems via computations of the critical groups [J].
Liu, Jinsheng ;
Wang, Shuli ;
Zhang, Jianming ;
Zhang, Fuwei .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (01) :60-71
[9]   Multiple solutions for boundary value problems of second-order difference equations with resonance [J].
Liu, Jinsheng ;
Wang, Shuli ;
Zhang, Jianming .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 374 (01) :187-196
[10]  
LIU JQ, 1989, J SYSTEMS SCI MATH S, V2, P32