Displaying similar documents to “The Schröder equation and asymptotic properties of linear delay differential equations.”

On the delay differential equation y'(x) = ay(τ(x)) + by(x)

Jan Čermák (1999)

Annales Polonici Mathematici

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The paper discusses the asymptotic properties of solutions of the scalar functional differential equation y ' ( x ) = a y ( τ ( x ) ) + b y ( x ) , x ∈ [ x 0 , ∞ ] . Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.

Asymptotic estimation for functional differential equations with several delays

Jan Čermák (1999)

Archivum Mathematicum

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We discuss the asymptotic behaviour of all solutions of the functional differential equation y ' ( x ) = ∑ i = 1 m a i ( x ) y ( τ i ( x ) ) + b ( x ) y ( x ) , where b ( x ) < 0 . The asymptotic bounds are given in terms of a solution of the functional nondifferential equation ∑ i = 1 m | a i ( x ) | ω ( τ i ( x ) ) + b ( x ) ω ( x ) = 0 .