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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: ...

Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

Domoshnitsky 0 Abraham Maghakyan 0 Roman Shklyar 0 Recommended by Marta A D Garc´ıa-Huidobro 0 Department of Mathematics and Computer Science, Ariel University Center of Samaria , Ariel 44837 , Israel We obtain