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

Abstract In this paper a method for studying stability of the equation x \u2033 ( t ) + \u2211 i = 1 m a i ( t ) x ( t \u2212 \u3c4 i ( t ) ) = 0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x \u2033 ( t ) + \u2211 i = 1 m a i ( t ) x ( t ) = 0 is not exponentially stable, the delay equation can be exponentially stable. MSC: 34K20, 34K06, 34K25