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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.

Everted equilibria of a spherical cap : a singular perturbation method

Andréa Schiaffino, Vanda Valente (1989)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Example of the Smooth Skew Product in the Plane with the One-dimensional Ramified Continuum as the Global Attractor*

L.S. Efremova (2012)

ESAIM: Proceedings

The example is constructed of the C1-smooth skew product of interval maps possessing the one-dimensional ramified continuum (containing no arcs homeomorphic to the circle) with an infinite set of ramification points as the global attractor.

Existence and global asymptotical stability of periodic solution for the $T$ -periodic logistic system with time-varying generating operators and $T_{0}$ -periodic impulsive perturbations on Banach spaces.

Wang, Jinrong, Xiang, X., Wei, W., Chen, Qian (2008)

Discrete Dynamics in Nature and Society

Existence and sharp asymptotic behavior of positive decreasing solutions of a class [4pt] of differential systems with power-type nonlinearities

Jaroslav Jaroš, Kusano Takaŝi (2014)

Archivum Mathematicum

The system of nonlinear differential equations $x^{'} + p_{1} (t) x^{α_{1}} + q_{1} (t) y^{β_{1}} = 0, y^{'} + p_{2} (t) x^{α_{2}} + q_{2} (t) y^{β_{2}} = 0, A$ is under consideration, where $α_{i}$ and $β_{i}$ are positive constants and $p_{i} (t)$ and $q_{i} (t)$ are positive continuous functions on $[a, \infty)$ . There are three types of different asymptotic behavior at infinity of positive solutions $(x (t), y (t))$ of (). The aim of this paper is to establish criteria for the existence of solutions of these three types by means of fixed point techniques. Special emphasis is placed on those solutions with both components decreasing to zero as $t \to \infty$ , which can be...

Existence and stability of measure differential equations

Purna Candra Das, Rishi Ram Sharma (1972)

Czechoslovak Mathematical Journal

Existence and stability of solutions for semilinear Dirichlet problems

Marek Galewski (2006)

Annales Polonici Mathematici

We provide existence and stability results for semilinear Dirichlet problems with nonlinearities satisfying some general local growth conditions. We derive a general abstract result which we then apply to prove the existence of solutions, their stability and continuous dependence on parameters for a sixth order ODE with Dirichlet type boundary data.

Existence and uniqueness for the predator-prey model with diffusion in the scalar case.

Julián López-Gómez, Rosa Pardo (1991)

Extracta Mathematicae

We solve the problem of the existence and uniqueness of coexistence states for the classical predator-prey model of Lotka-Volterra with diffusion in the scalar case.

Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation

Sergej S. Vojtenko (1987)

Kybernetika

Existence of doubly-weighted pseudo almost periodic solutions to non-autonomous differential equations.

Diagana, Toka (2011)

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

Existence of periodic solutions of impulsive differential systems.

Erbe, L.H., Liu, Xinzhi (1991)

Journal of Applied Mathematics and Stochastic Analysis

Existence of positive solutions of $n$ -dimensional system of nonlinear differential equations entering into a singular point

Josef Diblík, Miroslava Růžičková (2000)

Archivum Mathematicum

Existence of regularly and rapidly varying solutions for a class of third order nonlinear ordinary differential equations.

Jaroš, Jaroslav, Takaŝi, Kusano, Marić, Vojislav (2006)

Publications de l'Institut Mathématique. Nouvelle Série

Currently displaying 261 – 280 of 933

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Displaying 261 – 280 of 933

Estimates for Principal Lyapunov Exponents: A Survey

Estimates for the Cauchy matrix of perturbed linear impulsive equation.

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

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

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

Everted equilibria of a spherical cap : a singular perturbation method

Example of the Smooth Skew Product in the Plane with the One-dimensional Ramified Continuum as the Global Attractor*

Existence and global asymptotical stability of periodic solution for the $T$ -periodic logistic system with time-varying generating operators and $T_{0}$ -periodic impulsive perturbations on Banach spaces.

Existence and sharp asymptotic behavior of positive decreasing solutions of a class [4pt] of differential systems with power-type nonlinearities

Existence and stability of measure differential equations

Existence and stability of solutions for semilinear Dirichlet problems

Existence and uniqueness for the predator-prey model with diffusion in the scalar case.

Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation

Existence of doubly-weighted pseudo almost periodic solutions to non-autonomous differential equations.

Existence of periodic solutions of impulsive differential systems.

Existence of positive solutions of $n$ -dimensional system of nonlinear differential equations entering into a singular point

Existence of regularly and rapidly varying solutions for a class of third order nonlinear ordinary differential equations.

Existence of $ψ$ -bounded solutions for a system of differential equations.

Existence of $ψ$ -bounded solutions for nonhomogeneous linear differential equations.

Existence of $Ψ$ -bounded solutions for nonhomogeneous Lyapunov matrix differential equations on $ℝ$ .

Currently displaying 261 – 280 of 933