On the stability of strongly continuous semigroups of positive operators on
On the structure of the solution set of a functional-differential system on an unbounded interval
It is proved that under some conditions the set of all solutions of an initial value problem for -th order functional differential system on an unbounded interval is a compact .
On the terminal value problem for differential equations with deviating arguments
On the theory of functional-differential inclusions of neutral type.
On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space
In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an -set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].
On the uniform exponential stability of linear time-delay systems.
On the uniqueness of solutions of functional differential equations with nonincreasing right-hand sides
It is proved that nonincreasing and satisfying the Volterra condition right-hand side of a functional differential equation does not guarantee the uniqueness of solutions.
On the uniqueness of solutions to the weighted initial value problem for higher-order evolution singular functional-differential equations.
On the Vallée-Poussin problem for singular differential equations with deviating arguments
For the differential equation where the vector function has nonintegrable singularities with respect to the first argument, sufficient conditions for existence and uniqueness of the Vallée–Poussin problem are established.
On third order advanced nonlinear differential equations
On time transformations for differential equations with state-dependent delay
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.
On transformations of differential equations and systems with deviating argument
On transformations of functional-differential equations
The paper contains applications of Schrőder’s equation to differential equations with a deviating argument. There are derived conditions under which a considered equation with a deviating argument intersecting the identity can be transformed into an equation with a deviation of the form . Moreover, if the investigated equation is linear and homogeneous, we introduce a special form for such an equation. This special form may serve as a canonical form suitable for the investigation of oscillatory...
On transformations of functional-differential equations
On two transfer principles in stochastic differential geometry
On unbounded nonoscillatory solutions of systems of neutral differential equations
On unstable neutral differential equations of the second order
The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation to be oscillatory and to improve some existing results. The main results are based on the comparison principles.
On weak solutions of functional-differential abstract nonlocal Cauchy problems
The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.
On zero points of solutions of the -th order non-linear delay differential equation
On zeros of functions satisfying certain differential-difference equations