Infinitely many homoclinic solutions for a class of second-order Hamiltonian systems

被引：20

作者：

Chen, Huiwen ^{[1
]}

He, Zhimin ^{[1
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2014年

关键词：

Hamiltonian systems; homoclinic solutions; variational methods; critical points; CRITICAL-POINTS THEOREM; QUADRATIC POTENTIALS; PERIODIC-SOLUTIONS; ORBITS; MULTIPLICITY; EXISTENCE;

D O I：

10.1186/1687-1847-2014-161

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with the existence of infinitely many homoclinic solutions for a class of second-order Hamiltonian systems. By using the dual fountain theorem, we give some new criteria to guarantee that the second-order Hamiltonian systems have infinitely many homoclinic solutions. Some recent results are generalised and significantly improved.

引用

页数：15

共 35 条

[1]

[Anonymous], 1994, COMM APPL NONLINEAR

[2] ON AN ELLIPTIC EQUATION WITH CONCAVE AND CONVEX NONLINEARITIES [J].

BARTSCH, T ;

WILLEM, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (11) :3555-3561

[3] Multiple periodic solutions for Hamiltonian systems with not coercive potential [J].

Bonanno, Gabriele ;

Livrea, Roberto .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 363 (02) :627-638

[4] New results for perturbed Hamiltonian systems with impulses [J].

Chen, Huiwen ;

He, Zhimin .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (18) :9489-9497

[5] Infinitely many homoclinic solutions for nonautonomous p(t)-Laplacian Hamiltonian systems [J].

Chen, Peng ;

Tang, X. H. ;

Agarwal, Ravi P. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (04) :751-763

[6] Three periodic solutions for perturbed second order Hamiltonian systems [J].

Cordaro, Giuseppe ;

Rao, Giuseppe .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 359 (02) :780-785

[7]

Coti Zelati V., 1991, J. Am. Math. Soc., V4, P693, DOI 10.1090/S0894-0347-1991-1119200-3

[8] Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems [J].

Ding, Yanheng ;

Lee, Cheng .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (5-6) :1395-1413

[9] EXISTENCE AND MULTIPLICITY RESULTS FOR HOMOCLINIC SOLUTIONS TO A CLASS OF HAMILTONIAN-SYSTEMS [J].

DING, YH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 25 (11) :1095-1113

[10]

Guo CJ, 2014, MEM DIFFER EQU MATH, V61, P83

← 1 2 3 4 →