The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition

被引：0

作者：

Xiao, Yuming ^{[1
]}

Zhu, Gaosheng ^{[2
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[2] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2025年 / 414卷

关键词：

Hamiltonian systems; Periodic solutions; Minimal period; Nehari manifold; INDEX THEORY;

D O I：

10.1016/j.jde.2024.09.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the existence of periodic solutions with any prescribed minimal period T > 0 for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari set is not a manifold. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：348 / 371

页数：24

共 29 条

[11] SOME RESULTS ON SOLUTIONS OF MINIMAL PERIOD TO SUPERQUADRATIC HAMILTONIAN-SYSTEMS [J].

GIRARDI, M ;

MATZEU, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (05) :475-482

[12] SOLUTIONS OF MINIMAL PERIOD FOR A CLASS OF NONCONVEX HAMILTONIAN-SYSTEMS AND APPLICATIONS TO THE FIXED ENERGY PROBLEM [J].

GIRARDI, M ;

MATZEU, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1986, 10 (04) :371-382

[13] Iteration inequalities of the Maslov-type index theory with applications [J].

Liu, CG ;

Long, YM .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 165 (02) :355-376

[14]

Liu ZL, 2004, ADV NONLINEAR STUD, V4, P563

[15]

Long Y., 2002, Index Theory for Symplectic Paths with Applications, V207

[16] The Rabinowitz minimal periodic solution conjecture [J].

Long, Yiming .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2021, 32 (12)

[17] THE MINIMAL PERIOD PROBLEM OF PERIODIC-SOLUTIONS FOR AUTONOMOUS SUPERQUADRATIC 2ND-ORDER HAMILTONIAN-SYSTEMS [J].

LONG, YM .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 111 (01) :147-174

[18]

Long YM, 1997, CHINESE ANN MATH B, V18, P481

[19] THE MINIMAL PERIOD PROBLEM OF CLASSICAL HAMILTONIAN-SYSTEMS WITH EVEN POTENTIALS [J].

LONG, YM .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1993, 10 (06) :605-626

[20]

Mawhin J., 1989, Critical Point Theory and Hamilton System

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