Displaying similar documents to “Asymptotic properties of one differential equation with unbounded delay”

Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability

Josef Kalas, Josef Rebenda (2011)

Mathematica Bohemica

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We present several results dealing with the asymptotic behaviour of a real two-dimensional system x ' ( t ) = 𝖠 ( t ) x ( t ) + ∑ k = 1 m 𝖡 k ( t ) x ( θ k ( t ) ) + h ( t , x ( t ) , x ( θ 1 ( t ) ) , ⋯ , x ( θ m ( t ) ) ) with bounded nonconstant delays t - θ k ( t ) ≥ 0 satisfying lim t → ∞ θ k ( t ) = ∞ , under the assumption of instability. Here 𝖠 , 𝖡 k and h are supposed to be matrix functions and a vector function, respectively. The conditions for the instable properties of solutions together with the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the real system considered to one...