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Approximation of solutions of a difference-differential equation

B. G. Pachpatte (2010)

Archivum Mathematicum

In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.

Asymptotic properties of solutions of functional differential systems

Anatolij F. Ivanov, Pavol Marušiak (1992)

Mathematica Bohemica

In the paper we study the existence of nonoscillatory solutions of the system x i ( n ) ( t ) = j = 1 2 p i j ( t ) f i j ( x j ( h i j ( t ) ) ) , n 2 , i = 1 , 2 , with the property l i m t x i ( t ) / t k i = c o n s t 0 for some k i { 1 , 2 , ... , n - 1 } , i = 1 , 2 . Sufficient conditions for the oscillation of solutions of the system are also proved.

Attractors for non-autonomous retarded lattice dynamical systems

Tomás Caraballo, Francisco Morillas, José Valero (2015)

Nonautonomous Dynamical Systems

In this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Coordinate description of analytic relations

František Neuman (2006)

Mathematica Bohemica

In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.

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