SUBHARMONIC SOLUTIONS FOR A CLASS OF LAGRANGIAN SYSTEMS

被引：2

作者：

Bahrouni, Anouar ^{[1
]}

Izydorek, Marek ^{[2
]}

Janczewska, Joanna ^{[2
]}

机构：

[1] Univ Monastir, Dept Math, Fac Sci, Monastir 5019, Tunisia

[2] Gdansk Univ Technol, Fac Appl Phys & Math, Narutowicza 11-12, PL-80233 Gdansk, Poland

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2019年 / 12卷 / 07期

关键词：

Periodic solution; Lagrangian system; critical point; homoclinic orbit; HOMOCLINIC SOLUTIONS; HILBERT-SPACES; CONLEY INDEX; EXISTENCE; ORBITS;

D O I：

10.3934/dcdss.2019121

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that second order Hamiltonian systems -(u) over dot = V-u(t,u) with a potential V: R x R-N -> R of class C-1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [14]. Indeed, we weaken the latter condition in a neighbourhood of 0 is an element of R-N. We will also discuss when subharmonics pass to a nontrivial homoclinic orbit.

引用

页码：1841 / 1850

页数：10

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