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We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities $V_{3}$ and $V_{5}$ for a general smooth planar system.

Eighty fifth anniversary of birthday and scientific legacy of Professor Miloš Ráb

Ondřej Došlý, Eva Jansová, Josef Kalas (2014)

Archivum Mathematicum

The paper is concentrated on Professor Miloš Ráb and his contribution to the theory of oscillatory properties of solutions of second and third order linear differential equations, the theory of differential equations with complex coefficients and dynamical systems, and the theory of nonlinear second order differential equations. At the beginning, we take a brief look at the most important moments in his life. Afterwards, we describe his scientific activities on mentioned theories.

Ein Verfahren höherer Konvergenzordnung zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung.

E. Wagenführer (1976/1977)

Numerische Mathematik

Eine Bemerkung zu einem Satz von W. Hahn aus der Stabilitätstheorie linearer Systeme.

Harald K. Wimmer (1975)

Monatshefte für Mathematik

Energy decay estimates for Lienard's equation with quadratic viscous feedback.

Khapalov, Alexander Y., Nag, Parthasarathi (2003)

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

Entrée-sortie dans un tourbillon

Guy Wallet (1986)

Annales de l'institut Fourier

On étudie un champ de vecteurs lent-rapide de $R^{3}$ nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.

Entry into the sliding regime of solutions of nonautonomous operator equations.

Alidema, R.I. (1987)

Publications de l'Institut Mathématique. Nouvelle Série

Epidemiological Models and Lyapunov Functions

A. Fall, A. Iggidr, G. Sallet, J. J. Tewa (2010)

Mathematical Modelling of Natural Phenomena

We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio...

Equilibrium stability of a servo actuating flight controls in a servoelastic framework.

Ursu, Ioan, Ursu, Felicia, Halany, Andrei, Safta, Carmen Anca (2008)

Acta Universitatis Apulensis. Mathematics - Informatics

Error estimation for perturbed systems.

U. Kirchgraber (1976)

Journal für die reine und angewandte Mathematik

estabilidad de órbitas relativistas

Luciano Mora (1968)

Revista colombiana de matematicas

Estimates for Principal Lyapunov Exponents: A Survey

Janusz Mierczyński (2014)

Nonautonomous Dynamical Systems

This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....

Estimates for the Cauchy matrix of perturbed linear impulsive equation.

Simeonov, P.S., Bajnov, D.D. (1994)

International Journal of Mathematics and Mathematical Sciences

Estimates of the lower exponent of a two-dimensional linear system under Perron perturbations.

Izobov, N. (1997)

Memoirs on Differential Equations and Mathematical Physics

Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill

Alain Grigis (1987)

Annales scientifiques de l'École Normale Supérieure

Estimations of noncontinuable solutions of second order differential equations with $p$ -Laplacian

Eva Pekárková (2010)

Archivum Mathematicum

We study asymptotic properties of solutions for a system of second differential equations with $p$ -Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with $p$ -Laplacian ${(A (t) Φ_{p} (y^{'}))}^{'} + B (t) g (y^{'}) + R (t) f (y) = e (t)$ . Furthermore, we obtain results for a scalar equation.

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