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Asymptotic properties of third order functional dynamic equations on time scales

I. Kubiaczyk, S. H. Saker (2011)

Annales Polonici Mathematici

The purpose of this paper is to study the asymptotic properties of nonoscillatory solutions of the third order nonlinear functional dynamic equation [ p ( t ) [ ( r ( t ) x Δ ( t ) ) Δ ] γ ] Δ + q ( t ) f ( x ( τ ( t ) ) ) = 0 , t ≥ t₀, on a time scale , where γ > 0 is a quotient of odd positive integers, and p, q, r and τ are positive right-dense continuous functions defined on . We classify the nonoscillatory solutions into certain classes C i , i = 0,1,2,3, according to the sign of the Δ-quasi-derivatives and obtain sufficient conditions in order that C i = . Also, we establish...

Asymptotic properties of trinomial delay differential equations

Jozef Džurina, Renáta Kotorová (2008)

Archivum Mathematicum

The aim of this paper is to study asymptotic properties of the solutions of the third order delay differential equation 1 r ( t ) y ' ( t ) ' ' - p ( t ) y ' ( t ) + g ( t ) y ( τ ( t ) ) = 0 . * Using suitable comparison theorem we study properties of Eq. () with help of the oscillation of the second order differential equation.

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.

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