Behavior of the solutions to second order linear autonomous delay differential equations.
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.
We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order with impulses at fixed points.