## Abstract

We present some criteria for the oscillation of the second order nonlinear differential equation [*a(t)ψ(x(t))x'(t)*]' + *p(t)x'(t)* + *q(t)f (x(t))* =0, *t*≧*t*
_{0}> 0 with damping where *a*∈*C*
^{1} ([*t*
_{0},∞)) is a nonnegative function, *p, q*∈ C([*t*
_{0},∞)) are allowed to change sign on [*t*
_{0},∞), ψ, f∈*C*(**R**) with ψ(*x*) ≠ 0, *xf(x)*/ψ(*x*) > 0 for *x*≠ 0, and ψ, *f* have continuous derivatives on **R**{0} with [*f(x)* / ψ*(x)*]' ≧ 0 for *x*≠ 0. 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 ψ(*x*) is not required. Consequently, the obtained criteria cover new classes of equations to which known results do not apply.

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Manojlovič, J.V. Oscillation criteria for sublinear differential equations with damping.
*Acta Mathematica Hungarica* **104, **153–169 (2004). https://doi.org/10.1023/B:AMHU.0000034369.84782.0a

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- oscillation
- sublinear differential equation
- damping term
- integral averages