### A linear functional differential equation with distributions in the input.

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We show that if the Lyapunov exponents of a linear delay equation x′ = L(t)x t are limits, then the same happens with the exponential growth rates of the solutions to the equation x′ = L(t)x t + f(t, x t) for any sufficiently small perturbation f.

We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the...

We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular we show that a distribution independent stability region may be obtained in a similar way that delay independent...

This paper deals with property A and B of a class of canonical linear homogeneous delay differential equations of $n$-th order.

Sufficient conditions are established for the oscillation of proper solutions of the system $$\begin{array}{cc}\hfill {u}_{1}^{\text{'}}\left(t\right)& =p\left(t\right){u}_{2}\left(\sigma \left(t\right)\right)\phantom{\rule{0.166667em}{0ex}},\hfill \\ \hfill {u}_{2}^{\text{'}}\left(t\right)& =-q\left(t\right){u}_{1}\left(\tau \left(t\right)\right)\phantom{\rule{0.166667em}{0ex}},\hfill \end{array}$$ where $p,\phantom{\rule{0.166667em}{0ex}}q:{R}_{+}\to {R}_{+}$ are locally summable functions, while $\tau $ and $\sigma :{R}_{+}\to {R}_{+}$ are continuous and continuously differentiable functions, respectively, and $\underset{t\to +\infty}{lim}\tau \left(t\right)=+\infty $, $\underset{t\to +\infty}{lim}\sigma \left(t\right)=+\infty $.