A general method for the existence of periodic solutions of differential systems in the plane

被引：23

作者：

Fonda, Alessandro ^{[1
]}

Sfecci, Andrea ^{[2
]}

机构：

[1] Univ Trieste, Dipartimento Matemat & Informat, I-34127 Trieste, Italy

[2] SISSA Int Sch Adv Studies, I-34136 Trieste, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 252卷 / 02期

关键词：

Periodic solutions; Nonlinear dynamics; LANDESMAN-LAZER CONDITIONS; BOUNDARY-VALUE-PROBLEMS; ASYMMETRIC NONLINEARITIES; EQUATIONS;

D O I：

10.1016/j.jde.2011.08.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems "at resonance" are also considered, provided a Landesman-Lazer type of condition is assumed. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1369 / 1391

页数：23

共 50 条

[31] Existence and Regularity of Periodic Solutions for a Class of Partial Differential Operators
Bergamasco, Adalberto P.
Cavalcanti, Marcelo M.
Gonzalez, Rafael B.
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2021, 27 (03)
[32] On the Existence of Anti-periodic Solutions for Implicit Differential Equations
Liu, J.
Liu, Z.
ACTA MATHEMATICA HUNGARICA, 2011, 132 (03) : 294 - 305
[33] The existence of multiple positive periodic solutions for functional differential equations
Jiang, Weihua
APPLIED MATHEMATICS AND COMPUTATION, 2009, 208 (01) : 165 - 171
[34] Existence and Regularity of Periodic Solutions for a Class of Partial Differential Operators
Adalberto P. Bergamasco
Marcelo M. Cavalcanti
Rafael B. Gonzalez
Journal of Fourier Analysis and Applications, 2021, 27
[35] The existence of periodic solutions for a class of nonlinear functional differential equations
Jin-Zhi Liu
Zhi-Yuan Jiang
Ai-Xiang Wu
Applications of Mathematics, 2008, 53 : 97 - 103
[36] Existence and uniqueness of periodic solution for a class of differential systems
Yang, Xiaojing
Lo, Kueiming
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (01) : 36 - 46
[37] Dichotomy and existence of periodic solutions of quasilinear functional differential equations
Pinto, Manuel
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) : 1227 - 1234
[38] On the existence of periodic solutions of third order delay differential equations
Erdur, Sultan
Tunc, Cemil
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2023, 11 (02): : 319 - 331
[39] Existence and multiplicity of periodic solutions to differential equations with attractive singularities
Godoy, Jose
Hakl, Robert
Yu, Xingchen
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2022, 152 (02) : 402 - 427
[40] ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS
王克
Systems Science and Mathematical Sciences, 1990, (01) : 25 - 35

← 1 2 3 4 5 →