Oscillation in first order neutral differential equations with ''integrally small'' coefficients (Q1340557)

The authors obtain some new sufficient conditions for the oscillation of the solutions of the equation (1) below without the restrictive hypothesis \(\int^{+\infty}_ 0 [P(s)- Q(s- \tau-\delta)] ds= +\infty\). \[ {d\over dt} [x(t)- R(t) x(t- r)]+ P(t) x(t- \tau)- Q(t) x(t-\delta)= 0,\tag{1} \] where \(P,Q,R\in C([t_ 0; +\infty),\mathbb{R}^ +)\), \(r> 0\) and \(\tau,\delta\geq 0\).