A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions
From MaRDI portal
Publication:2300430
DOI10.1016/j.jde.2019.11.032zbMath1436.34036arXiv1606.04776OpenAlexW2990594273MaRDI QIDQ2300430
Publication date: 27 February 2020
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.04776
Periodic solutions to ordinary differential equations (34C25) Nonautonomous smooth dynamical systems (37C60)
Related Items (5)
Centers and limit cycles for a family of Abel equations ⋮ Upper bounds of limit cycles in Abel differential equations with invariant curves ⋮ Characterization of the existence of non-trivial limit cycles for generalized Abel equations ⋮ Planar systems and Abel equations ⋮ On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique
Cites Work
- Unnamed Item
- Unnamed Item
- Existence of non-trivial limit cycles in Abel equations with symmetries
- Periodic solutions for equation \(\dot x = A(t)x^m + B(t)x^n + C(t)x^l\) with \(A(t)\) and \(B(t)\) changing signs
- Limit cycles of Abel equations of the first kind
- A new Chebyshev family with applications to Abel equations
- Estimates on the number of limit cycles of a generalized Abel equation
- Periodic orbits in complex Abel equations
- A new uniqueness criterion for the number of periodic orbits of Abel equations
- Iterative approximation of limit cycles for a class of Abel equations
- On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
- Cubic systems and Abel equations
- On the diversity of Poincaré mappings for cubic equations with variable coefficients
- Limit cycles of non-autonomous scalar ODEs with two summands
- The number of periodic solutions of polynomial differential equations
- Abel-like differential equations with no periodic solutions
- Harvesting in seasonal environments
- Limit Cycles for a Class of Abel Equations
- Qualitative Tools for Studying Periodic Solutions and Bifurcations as Applied to the Periodically Harvested Logistic Equation
- On a Class of Differential Equations of Riccati Type
- A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
- The Bautin ideal of the Abel equation
- Generalized centre conditions and multiplicities for polynomial Abel equations of small degrees
- Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions
- The Number of Periodic Solutions of the Equation Ż=z N +p 1 (t )z N −1 +…+p N (t )
- LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS
- LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS
This page was built for publication: A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions