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A Perron-type theorem for nonautonomous delay equations

Luis Barreira, Claudia Valls (2013)

Open Mathematics

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.

About differential inequalities for nonlocal boundary value problems with impulsive delay equations

Alexander Domoshnitsky, Irina Volinsky (2015)

Mathematica Bohemica

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...

Approximating the Stability Region for a Differential Equation with a Distributed Delay

S. A. Campbell, R. Jessop (2009)

Mathematical Modelling of Natural Phenomena

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...

Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments

Roman Koplatadze, N. L. Partsvania, Ioannis P. Stavroulakis (2003)

Archivum Mathematicum

Sufficient conditions are established for the oscillation of proper solutions of the system u 1 ' ( t ) = p ( t ) u 2 ( σ ( t ) ) , u 2 ' ( t ) = - q ( t ) u 1 ( τ ( t ) ) , where p , q : R + R + are locally summable functions, while τ and σ : R + R + are continuous and continuously differentiable functions, respectively, and lim t + τ ( t ) = + , lim t + σ ( t ) = + .

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