On some constants for oscillation and stability of delay equations

Abstract

We discuss the famous constants of 1 / e 1/e , 1, 3 / 2 3/2 in necessary and/or sufficient oscillation and stability conditions for delay differential equations with one or more delays: \[ x ′ ( t ) = − ∑ k = 1 m a k ( t ) x ( t − h k ( t ) ) , x^{\prime }(t)= - \sum _{k=1}^ma_k(t) x(t-h_k(t)), \] including equations with oscillatory coefficients. Some counterexamples (which refer to necessary oscillation and stability conditions) are presented and open problems are stated.