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In this paper, we prove and discuss averaging results for ordinary differential equations perturbed by a small parameter. The conditions we assume on the right-hand sides of the equations under which our averaging results are stated are more general than those considered in the literature. Indeed, often it is assumed that the right-hand sides of the equations are uniformly bounded and a Lipschitz condition is imposed on them. Sometimes this last condition is relaxed to the uniform continuity in...
This contribution is devoted to the problem of asymptotic behaviour of solutions of scalar linear differential equation with variable bounded delay of the form
with positive function Results concerning the structure of its solutions are obtained with the aid of properties of solutions of auxiliary homogeneous equation
where the function is positive. A result concerning the behaviour of solutions of Eq. (*) in critical case is given and, moreover, an analogy with behaviour of solutions of...
We discuss the effect of time delay on blow-up of solutions to initial-boundary value problems for nonlinear reaction-diffusion equations. Firstly, two examples are given, which indicate that the delay can both induce and prevent the blow-up of solutions. Then we show that adding a new term with delay may not change the blow-up character of solutions.
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