Displaying similar documents to “Special solutions of neutral functional differential equations.”

Behaviour of solutions of linear differential equations with delay

Josef Diblík (1998)

Archivum Mathematicum

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This contribution is devoted to the problem of asymptotic behaviour of solutions of scalar linear differential equation with variable bounded delay of the form x ˙ ( t ) = - c ( t ) x ( t - τ ( t ) ) ( * ) with positive function c ( t ) . Results concerning the structure of its solutions are obtained with the aid of properties of solutions of auxiliary homogeneous equation y ˙ ( t ) = β ( t ) [ y ( t ) - y ( t - τ ( t ) ) ] where the function β ( t ) is positive. A result concerning the behaviour of solutions of Eq. (*) in critical case is given and, moreover, an analogy with behaviour of...