Oscillatory property of solutions for second order functional differential equation to be changed into an ``integrally small'' coefficient (Q810247)

The author considers the oscillatory property of the second order functional differential equation \((1)\quad (r(t)\psi (x)x')'+p(t)f(x(q(t)))=0,\quad t\geq t_ 0\geq 0,\) \(('=d/dt)\) where \(r\in C'([t_ 0,\infty);(0,\infty))\), p(t)\(\geq 0\), and \(\int^{\infty}_{t_ 0}(1/r(t))dt=\infty\). Five oscillation theorems for the equation (1) are obtained by establishing and using a lemma.