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W-transform for exponential stability of second order delay differential equations without damping terms

In this paper a method for studying stability of the equation x ″ ( t ) + ∑ i = 1 m a i ( t ) x ( t − τ i ( t ) ) = 0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x ″ ( t ) + ∑ i = 1 m a i ( t ) x ( t ) = 0 is not exponentially stable, the delay equation can be exponentially stable. MSC: ...

A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia

In this paper, we propose and analyze a mathematical model for the treatment of chronic myelogenous (myeloid) leukemia (CML), a cancer of the blood. Our main focus is on the combined treatment of CML based on imatinib therapy and immunotherapy. Treatment with imatinib is a molecular targeted therapy that inhibits the cells involved in the chronic CML pathogenesis. Immunotherapy ...

A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia

In this paper, we propose and analyze a mathematical model for the treatment of chronic myelogenous (myeloid) leukemia (CML), a cancer of the blood. Our main focus is on the combined treatment of CML based on imatinib therapy and immunotherapy. Treatment with imatinib is a molecular targeted therapy that inhibits the cells involved in the chronic CML pathogenesis. Immunotherapy ...

On a delay population model with quadratic nonlinearity

A nonlinear delay differential equation with quadratic nonlinearity, x ˙ ( t ) = r ( t ) [ ∑ k = 1 m α k x ( h k ( t ) ) − β x 2 ( t ) ] , t ≥ 0 , is considered, where α k and β are positive constants, h k : [ 0 , ∞ ) → R are continuous functions such that t − τ ≤ h k ( t ) ≤ t , τ = const , τ > 0 , for any t > 0 the inequality h k ( t ) 0 . It is proved that the positive ...

On a delay population model with quadratic nonlinearity

A nonlinear delay differential equation with quadratic nonlinearity, x ˙ ( t ) = r ( t ) [ ∑ k = 1 m α k x ( h k ( t ) ) − β x 2 ( t ) ] , t ≥ 0 , is considered, where α k and β are positive constants, h k : [ 0 , ∞ ) → R are continuous functions such that t − τ ≤ h k ( t ) ≤ t , τ = const , τ > 0 , for any t > 0 the inequality h k ( t ) 0 . It is proved that the positive ...

Exponential Stability of Difference Equations with Several Delays: Recursive Approach

Leonid Berezansky 1 Elena Braverman 0 0 Department of Mathematics and Statistics, University of Calgary , 2500 University Drive N.W., Calgary AB , Canada T2N 1N4 1 Department of Mathematics, Ben

On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay

,s X h s ,t0 x t0 X h s ,ξ g ξ dξ ds g t X˙ t,s g s ds K t,s X h s ,ξ g ξ dξds. we obtain X˙ t, s s g t . 2.21 Acknowledgments Leonid Berezansky was partially supported by grant 25/5 “Systematic