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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 20
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 6, December 2013
  4. Extended quasi-homogeneous polynomial system in $${\mathbb{R}^{3}}$$
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 6, December 2013
An existence result for evolution equations in non-cylindrical domains
$${W^{1,1}_0}$$ -solutions for elliptic problems having gradient quadratic lower order terms
A remark on the existence of slowly growing positive solutions to second order super-linear ordinary differential equations
Extended quasi-homogeneous polynomial system in $${\mathbb{R}^{3}}$$
An anisotropic eigenvalue problem of Stekloff type and weighted Wulff inequalities
Multiple positive solutions of singular and critical elliptic problem in $${\mathbb{R}^2}$$ with discontinuous nonlinearities
Unconditional global well-posedness for the 3D Gross-Pitaevskii equation for data without finite energy
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 5, October 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 4, August 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 3, June 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 2, April 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 1, February 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Extended quasi-homogeneous polynomial system in $${\mathbb{R}^{3}}$$

Content Provider SpringerLink
Author Zhao, Yulin Huang, Jianfeng
Copyright Year 2013
Abstract In this paper we define an extended quasi-homogeneous polynomial system d x/dt = Q = Q 1 + Q 2 + ... + Q δ , where Q i are some 3-dimensional quasi-homogeneous vectors with weight α and degree i, i = 1, . . . ,δ. Firstly we investigate the limit set of trajectory of this system. Secondly let Q T be the projective vector field of Q. We show that if δ ≤ 3 and the number of closed orbits of Q T is known, then an upper bound for the number of isolated closed orbits of the system is obtained. Moreover this upper bound is sharp for δ = 3. As an application, we show that a 3-dimensional polynomial system of degree 3 (resp. 5) admits 26 (resp. 112) isolated closed orbits. Finally, we prove that a 3-dimensional Lotka-Volterra system has no isolated closed orbits in the first octant if it is extended quasi-homogeneous.
Ending Page 1794
Page Count 24
Starting Page 1771
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 6
Volume Number 20
Language English
Publisher Springer Basel
Publisher Date 2013-05-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Periodic orbits of vector fields and flows Analysis Attractors and repellers, topological structure Vector fields, flows, ordinary differential equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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