On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions

被引：15

作者：

Costa, David G. ^{[1
]}

Tehrani, Hossein ^{[1
]}

机构：

[1] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 412卷 / 01期

关键词：

Singular Hamiltonian system; Homoclinic solution; Periodic coefficients; Category theory; Strong-Force condition; ORBITS; POTENTIALS; MULTIPLICITY; EXISTENCE; CATEGORY; SPACE;

D O I：

10.1016/j.jmaa.2013.10.056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show existence of infinitely many homoclinic orbits at the origin for a class of singular second-order Hamiltonian systems ii + V-u(t,u) = 0, -infinity < t < infinity. We use variational methods under the assumption that V(t, u) satisfies the so-called "Strong-Force" condition. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：200 / 211

页数：12

共 22 条

[1]

Ambrosetti A., 1993, Progr. Nonlinear Differential Equations Appl., V10

[2]

[Anonymous], 1994, COMM APPL NONLINEAR

[3] A MINIMAX METHOD FOR A CLASS OF HAMILTONIAN-SYSTEMS WITH SINGULAR POTENTIALS [J].

BAHRI, A ;

RABINOWITZ, PH .

JOURNAL OF FUNCTIONAL ANALYSIS, 1989, 82 (02) :412-428

[4] Multiplicity of homoclinic solutions for singular second-order conservative systems [J].

Bertotti, ML ;

Jeanjean, L .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1996, 126 :1169-1180

[5] MULTIPLE HOMOCLINIC ORBITS FOR AUTONOMOUS, SINGULAR POTENTIALS [J].

BESSI, U .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1994, 124 :785-802

[6] Heteroclinic and homoclinic solutions for a singular Hamiltonian system [J].

Borges, Maria Joao .

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2006, 17 :1-32

[7] Homoclinics and heteroclinics for a class of conservative singular Hamiltonian systems [J].

Caldiroli, P ;

Jeanjean, L .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 136 (01) :76-114

[8] Multiple homoclinics for a class of singular Hamiltonian systems [J].

Caldiroli, P ;

DeCoster, C .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 211 (02) :556-573

[9] EXISTENCE AND MULTIPLICITY OF HOMOCLINIC ORBITS FOR POTENTIALS ON UNBOUNDED-DOMAINS [J].

CALDIROLI, P .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1994, 124 :317-339

[10]

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

← 1 2 3 →