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On the limits of solutions of functional differential equations

Mihály Pituk — 1993

Mathematica Bohemica

Our aim in this paper is to obtain sufficient conditions under which for every $ξ \in R^{n}$ there exists a solution $x$ of the functional differential equation $\dot{x} (t) = \int_{c}^{t} [d_{s} Q (t, s)] f (t, x (s)), t \in [t_{0}, T]$ such that $l i m_{t \to T -} x (t) = ξ$ .

Adjoint operators and boundary value problems for linear differential equations

Mihály Pituk — 1991

Mathematica Slovaca

Convergence to equilibria in a differential equation with small delay

Mihály Pituk — 2002

Mathematica Bohemica

Consider the delay differential equation $\dot{x} (t) = g (x (t), x (t - r)), (1)$ where $r > 0$ is a constant and $g ℝ^{2} \to ℝ$ is Lipschitzian. It is shown that if $r$ is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.

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On the limits of solutions of functional differential equations

Adjoint operators and boundary value problems for linear differential equations

Convergence to equilibria in a differential equation with small delay

Convergence to equilibria in a differential equation with small delay

Special solutions of neutral functional differential equations.

Asymptotic estimates and exponential stability for higher-order monotone difference equations.

Exponential stability in a scalar functional differential equation.

Asymptotic expansions for higher-order scalar difference equations.