Oscillations in Second Order Linear Autonomous Differential Equations with Distributed Type Deviating Arguments

A class of second order linear autonomous differential equations with distributed type deviating arguments is considered. It is proved that a necessary and sufficient condition for the oscillation of all solutions is that the associated characteristic equation have no real roots, The proof is based on the method of the Laplace transforms, using a known result about the abscissa of convergence of the Laplace transform of a nonnegative function,