Oscillation criteria for sublinear differential equations with damping (Q558258)

In this paper are presented some criteria for the oscillation of the second order nonlinear differential equation \[ [a(t)\psi(\chi(t))\chi'(t)]'+p(t)\chi'(t)+q(t)f(\chi(t))=0\quad t\geq t_0>0 \] with damping. This criteria are obtained by using a general class of the parameter functions \(H(t,s)\) in the averaging techniques. An essential feature of the proved results is that the assumption of positivity of the function \(\psi(\chi(t))\) is not required. Conversely, the obtained criteria cover new classes of equations to which known results do not apply.