Displaying similar documents to “Asymptotic estimation of the convergence of solutions of the equation x ˙ ( t ) = b ( t ) x ( t - τ ( t ) ) ”

Asymptotic properties of an unstable two-dimensional differential system with delay

Josef Kalas (2006)

Mathematica Bohemica

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The asymptotic behaviour of the solutions is studied for a real unstable two-dimensional system x ' ( t ) = 𝖠 ( t ) x ( t ) + 𝖡 ( t ) x ( t - r ) + h ( t , x ( t ) , x ( t - r ) ) , where r > 0 is a constant delay. It is supposed that 𝖠 , 𝖡 and h are matrix functions and a vector function, respectively. Our results complement those of Kalas [Nonlinear Anal. 62(2) (2005), 207–224], where the conditions for the existence of bounded solutions or solutions tending to the origin as t → ∞ are given. The method of investigation is based on the transformation of the real system considered...