86 research outputs found
On oscillation of a Volterra integral equation with delay
AbstractThe purpose of this paper is to obtain sufficient conditions for oscillation of all solutions of the equation x(t) = f(t) + ∝at K(t, s, x(s), x(g(s))) ds to study the behaviour of its oscillatory solutions in a dependence on the distance between their consecutive zeros and to establish a theorem for localization of the zeros of its solutions
Asymptotic stability of the solutions of a linear singularly perturbed system with unbounded delay
AbstractSufficient conditions for asymptotic stability of the solutions of a linear singularly perturbed system of differential equations with unbounded delay have been found. Under the same conditions it is proved that for a locally Lipschitz initial function the initial value problem for the system degenerates regularly
Second method of Lyapunov and comparison principle for systems with impulse effect
AbstractIn the present paper questions of stability and boundedness of the solutions of systems with impulse effect at fixed moments with respect to a manifold are considered. The investigations are carried out by means of piecewise continuous vector-valued functions which are analogues of Lyapunov's functions. By means of a vector comparison equation and differential inequalities for piecewise continuous functions, theorems of stability and boundedness of the solutions of systems with impulses with respect to a manifold have been obtained
Exponential stability of the solutions of the initial-value problem for systems with impulse effect
AbstractIn the present paper conditions have been found under which the exponential stability of a given solution of a system with impulse effect follows from the exponential stability of the respective system in variations
Exponential stability of the solutions of singularly perturbed systems with impulse effect
AbstractIn the present paper the exponential stability of the solutions of singularly perturbed systems with impulse effect is investigated. In order to obtain the main results the comparison method and piecewise continuous auxiliary functions which are analogues of Lyapunov's functions are used
Oscillatory and Asymptotic Properties of the Solutions of a Class of Operator-Differential Equations
Sin resume
Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations
AbstractIn the present paper, by means of a suitable comparison lemma sufficient conditions for uniform Lipschitz stability of an arbitrary solution of an impulsive system of differential-difference equations with variable impulsive perturbations are obtained
Application of the averaging method for the solution of boundary problems for ordinary differential and integro-differential equations
Lipschitz stability of linear impulsive differential-difference equations
Sufficient conditions are found for the Lipschitz stability of linear impulsive differential-difference equations.The impulses are realized at fixed moments
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