Limit Cycles for a Class of Abel Equations
From MaRDI portal
Publication:3359064
DOI10.1137/0521068zbMath0732.34025OpenAlexW2034478771MaRDI QIDQ3359064
Publication date: 1990
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0521068
limit cyclesperiodic solutionRiccati equationAbel differential equationpolynomial vector fieldcentreperiodic solutions second kind
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
Related Items (79)
On the limit cycles of polynomial differential systems with homogeneous nonlinearities ⋮ Periodic solutions of linear, Riccati, and Abel dynamic equations ⋮ Uniqueness of limit cycles for polynomial first-order differential equations ⋮ Uniqueness of limit cycles for quadratic vector fields ⋮ LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS ⋮ Rational Periodic Solutions on Some Generalized Abel Equations ⋮ LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS ⋮ Periodic orbits in complex Abel equations ⋮ Existence of closed solutions for a polynomial first order differential equation ⋮ Centers and limit cycles for a family of Abel equations ⋮ A cubic nonlinear population growth model for single species: theory, an explicit-implicit solution algorithm and applications ⋮ Polynomial solutions of equivariant polynomial Abel differential equations ⋮ A new uniqueness criterion for the number of periodic orbits of Abel equations ⋮ Rational solutions of Abel trigonometric polynomial differential equations ⋮ A uniqueness criterion of limit cycles for planar polynomial systems with homogeneous nonlinearities ⋮ Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities ⋮ Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves ⋮ Chini equations and isochronous centers in three-dimensional differential systems ⋮ Existence of non-trivial limit cycles in Abel equations with symmetries ⋮ Cubic nonlinear differential system, their periodic solutions and bifurcation analysis ⋮ Centers and isochronous centers for two classes of generalized seventh and ninth systems ⋮ Some families of quadratic systems with at most one limit cycle ⋮ Stability of singular limit cycles for Abel equations revisited ⋮ Conditions to the existence of center for Abel equations ⋮ 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 ⋮ Trigonometric polynomial solutions of Bernoulli trigonometric polynomial differential equations ⋮ Existence of at most two limit cycles for some non-autonomous differential equations ⋮ Bifurcation of a Kind of 1D Piecewise Differential Equation and Its Application to Piecewise Planar Polynomial Systems ⋮ Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities. ⋮ A new Chebyshev family with applications to Abel equations ⋮ Limit cycles of Abel equations of the first kind ⋮ 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 ⋮ Stability of singular limit cycles for Abel equations ⋮ Bifurcation of a Kind of Piecewise Smooth Generalized Abel Equation via First and Second Order Analyses ⋮ On the number of limit cycles of some systems on the cylinder ⋮ On the polynomial solutions of the polynomial differential equations \({y \; y}' = a_0(x) + a_1(x) y + a_2(x) y^2 + \ldots + a_n(x) y^{n}\) ⋮ On the number of limit cycles of a generalized Abel equation ⋮ Parametric centers for trigonometric Abel equations ⋮ Integrability, degenerate centers, and limit cycles for a class of polynomial differential systems ⋮ HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS ⋮ On the polynomial limit cycles of polynomial differential equations ⋮ Darboux integrability and algebraic limit cycles for a class of polynomial differential systems ⋮ Lower bounds for the number of limit cycles of trigonometric Abel equations ⋮ Abel-like differential equations with no periodic solutions ⋮ Abel-like differential equations with a unique limit cycle ⋮ Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities ⋮ Periodic solutions with nonconstant sign in Abel equations of the second kind ⋮ Cauchy-type integrals of algebraic functions ⋮ Limit cycles for rigid cubic systems ⋮ Some new results on Abel equations ⋮ Center and composition conditions for Abel differential equation, and rational curves ⋮ Limit cycles for cubic systems with a symmetry of order 4 and without infinite critical points ⋮ Center conditions at infinity for Abel differential equations ⋮ On the rational limit cycles of Abel equations ⋮ Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields ⋮ Rational limit cycles of Abel equations ⋮ Iterative approximation of limit cycles for a class of Abel equations ⋮ The number of polynomial solutions of polynomial Riccati equations ⋮ Algebraic geometry of Abel differential equation ⋮ Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities ⋮ A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions ⋮ Planar nonautonomous polynomial equations II. Coinciding sectors ⋮ On the study and application of limit cycles of a kind of piecewise smooth equation ⋮ Some open problems in low dimensional dynamical systems ⋮ Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems ⋮ On the Number of Limit Cycles in Generalized Abel Equations ⋮ The number of limit cycles in planar systems and generalized Abel equations with monotonous hyperbolicity ⋮ Existence of closed solutions of an equation \(\dot x=f(t,x)\), where \(f_x'(t,x)\) is weakly convex or concave in \(x\) ⋮ Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ The method of holomorphic foliations in planar periodic systems: The case of Riccati equations ⋮ Rational limit cycles on generalized Bernouilli polynomial equations ⋮ A new Chebyshev criterion and its application to planar differential systems ⋮ BIFURCATION OF ONE-PARAMETER PERIODIC ORBITS OF THREE-DIMENSIONAL DIFFERENTIAL SYSTEMS ⋮ On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique ⋮ Criteria on the existence of limit cycles in planar polynomial differential systems ⋮ Limit cycles for 3-monomial differential equations ⋮ On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones
This page was built for publication: Limit Cycles for a Class of Abel Equations
