MULTIPLE PERIODIC SOLUTIONS FOR ONE-SIDED SUBLINEAR SYSTEMS: A REFINEMENT OF THE POINCARE-BIRKHOFF APPROACH

被引：5

作者：

Donde, Tobia ^{[1
]}

Zanolin, Fabio ^{[1
]}

机构：

[1] Univ Udine, Dept Math Comp Sci & Phys, Via Sci 206, I-33100 Udine, Italy

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2020年 / 55卷 / 02期

关键词：

Poincare-Birkhoff theorem; bend-twist maps; topological horseshoes; periodic solutions; complex oscillations; SUBHARMONIC SOLUTIONS; THEOREM; EQUATIONS;

D O I：

10.12775/TMNA.2019.104

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 multiple periodic (harmonic and subharmonic) solutions for a class of planar Hamiltonian systems which includes the case of the second order scalar ODE x '''' + a(t)g(x) = 0 with g satisfying a one-sided condition of sublinear type. We consider the classical approach based on the Poincare-Birkhoff fixed point theorem as well as some refinements on the side of the theory of topological horseshoes. A Duffing-type equation and an exponential nonlinearity case are studied as applications.

引用

页码：565 / 581

页数：17

共 10 条

[1] Sign-Changing Subharmonic Solutions to Unforced Equations with Singular φ-Laplacian [J].

Boscaggin, Alberto ;

Garrione, Maurizio .

DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATI ONS, 2013, 47 :321-329

[2]

Boscaggin A, 2011, ADV NONLINEAR STUD, V11, P77

[3] CONTINUABILITY OF SOLUTIONS OF SECOND ORDER DIFFERENTIAL EQUATIONS [J].

BURTON, T ;

GRIMMER, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 29 (02) :277-&

[4] ON CONTINUATION OF SOLUTIONS OF A CERTAIN NON-LINEAR DIFFERENTIAL EQUATION [J].

COFFMAN, CV ;

ULLRICH, DF .

MONATSHEFTE FUR MATHEMATIK, 1967, 71 (05) :385-&

[5] PERIODIC-SOLUTIONS OF DUFFINGS EQUATIONS WITH SUPERQUADRATIC POTENTIAL [J].

DING, T ;

ZANOLIN, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 97 (02) :328-378

[6] A higher dimensional Poincare-Birkhoff theorem for Hamiltonian flows [J].

Fonda, Alessandro ;

Urena, Antonio J. .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2017, 34 (03) :679-698

[7] MINIMIZATION PROBLEMS FOR NONCOERCIVE FUNCTIONALS SUBJECT TO CONSTRAINTS [J].

LE, VK ;

SCHMITT, K .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (11) :4485-4513

[8] Maslov index, Poincare-Birkhoff theorem and periodic solutions of asymptotically linear planar Hamiltonian systems [J].

Margheri, A ;

Rebelo, C ;

Zanolin, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 183 (02) :342-367

[9]

Papini D, 2004, ADV NONLINEAR STUD, V4, P71

[10] A note on the Poincare-Birkhoff fixed point theorem and periodic solutions of planar systems [J].

Rebelo, C .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 29 (03) :291-311

← 1 →