## On the oscillation of certain third order nonlinear functional differential equations.(English)Zbl 1154.34368

Summary: We offer some sufficient conditions for the oscillation of all solutions of third order nonlinear functional differential equations of the form
$\frac{d}{dt}\left(a(t)\left(\frac{d^2}{dt^2}\;x(t)\right)^\alpha\right)+q(t)f(x[g(t)])=0$
and
$\frac{d}{dt} \left(a(t)\left(\frac{d^2}{dt^2}\;x(t)\right)^\alpha\right)= q(t)f(x[g(t)])+ p(t)h(x[\sigma(t)]),$
when $$\int^\infty a^{-1/\alpha}(s)\,ds < \infty$$. The case when $$\int^\infty a^{-1/\alpha}(s)\,ds =\infty$$ is also included.

### MSC:

 34K11 Oscillation theory of functional-differential equations
Full Text:

### References:

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