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Displaying 101 – 120 of 240

On first integrals for polynomial differential equations on the line

Henryk Żołądek (1993)

Studia Mathematica

We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral.

On functions describing a distribution of zeros of solutions of an iterated linear differential equation of the fourth order

Vladimír Vlček (1979)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

On holomorphic foliations without algebraic solutions.

Coutinho, S. C., Ribeiro, Bruno F. M. (2001)

Experimental Mathematics

On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems

Aziza Berbache (2023)

Mathematica Bohemica

We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center. We show that when these piecewise differential systems are continuous, they can have at most one limit cycle. However, when the piecewise differential systems are discontinuous, we show that they can have at most two limit cycles, and that there exist such systems with two limit cycles. Therefore, in particular, we...

On plane polynomial vector fields and the Poincaré problem.

El Kahoui, M'hammed (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On solutions of the Lagerstrom equation

Božo Vrdoljak (1988)

Archivum Mathematicum

On the approximation of the limit cycles function.

Cherkas, L., Grin, A., Schneider, K.R. (2007)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

On the center of the generalized Liénard system

Cheng Dong Zhao, Qi-Min He (2002)

Czechoslovak Mathematical Journal

In this paper, we discuss the conditions for a center for the generalized Liénard system $\frac{d x}{d t} = ϕ (y) - F (x), \frac{d y}{d t} = - g (x),$ or $\frac{d x}{d t} = ψ (y), \frac{dy}{d t} = - f (x) h (y) - g (x),$ with $f (x)$ , $g (x)$ , $ϕ (y)$ , $ψ (y)$ , $h (y) ℝ \to ℝ$ , $F (x) = \int_{0}^{x} f (x) d x$ , and $x g (x) > 0$ for $x \neq 0$ . By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2].

On the composition conjectures.

Alwash, Mohamad A. M. (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination.

De La Sen, M., Agarwal, Ravi P., Ibeas, A., Alonso-Quesada, S. (2011)

Advances in Difference Equations [electronic only]

On the focal points of solutions of a certain fourth order differential equation

Vladimír Vlček (1986)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On the limit cycle of the Liénard equation

Kenzi Odani (2000)

Archivum Mathematicum

In the paper, we give an existence theorem of periodic solution for Liénard equation $\dot{x} = y - F (x)$ , $\dot{y} = - g (x)$ . As a result, we estimate the amplitude $ρ (μ)$ (maximal $x$ -value) of the limit cycle of the van der Pol equation $\dot{x} = y - μ (x^{3} / 3 - x)$ , $\dot{y} = - x$ from above by $ρ (μ) < 2.3439$ for every $μ \neq 0$ . The result is an improvement of the author’s previous estimation $ρ (μ) < 2.5425$ .

On the limit cycle of the van der Pol equation

Odani, Kenzi (1998)

Proceedings of Equadiff 9

On the Limit-Point and Strong Limit-Point Classification of 2 n-th Order Differential Expressions with Widly Oscillating Coefficients.

B. Malcom Brown, W. Desmond Evans (1973)

Mathematische Zeitschrift

On the number of limit cycles in perturbations of a two dimensional nonlinear differential system.

Josef Hainzl (1997)

Aequationes mathematicae

On the Poincaré-Lyapunov constants and the Poincare series

Jaume Giné, Xavier Santallusia (2001)

Applicationes Mathematicae

For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...

On $ω$ -limit sets of nonautonomous differential equations

Boris S. Klebanov (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper the $ω$ -limit behaviour of trajectories of solutions of ordinary differential equations is studied by methods of an axiomatic theory of solution spaces. We prove, under very general assumptions, semi-invariance of $ω$ -limit sets and a Poincar’e-Bendixon type theorem.

One-parameter family of cubic Kolmogorov system with an isochronous center.

E. Sáez, I. Szántó (1997)

Collectanea Mathematica

We show the existence of a one-parameter family of cubic Kolmogorov system with an isochronous center in the realistic quadrant.

Orbites Hétérocliniques au Voisinage d'une Bifurcation de Poincaré Dégénérée pour les Champs de Vecteurs de ...

René-Louis Clerc, Christian Hartmann, Boniface Razafimandimby (1989)

Monatshefte für Mathematik

Oscillatory properties of some classes of nonlinear differential equations

Milan Medveď (1992)

Mathematica Bohemica

A sufficient condition for the nonoscillation of nonlinear systems of differential equations whose left-hand sides are given by $n$ -th order differential operators which are composed of special nonlinear differential operators of the first order is established. Sufficient conditions for the oscillation of systems of two nonlinear second order differential equations are also presented.

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