Damped second order linear differential equation with deviating arguments: Sharp results in oscillation properties

This article presents a new approach for investigating the oscillation properties of second order linear differential equations with a damped term containing a deviating argument $$ x''(t)-[P(t)x(r(t))]'+Q(t)x(l(t))=0,quad r(t)leq t. $$ To study this equation, a specially adapted version of Sturmian Comparison Method is developed and the following results are obtained: