Nonoscillation and Exponential Stability of Delay Differential Equations with Oscillating Coefficients

摘要

We prove that under some additional conditions, the nonoscillation of the scalar delay differential equation $$ dot xleft( t right) + sumlimits_{k = 1}^m {a_k left( t right)xleft( {h_k left( t right)} right) = 0} $$ implies the exponential stability. New nonoscillation conditions are obtained for equations with positive and negative coefficients and for equations of arbitrary signs. As an example, we present an exponentially stable equation with two delays and two oscillating coefficients.