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On the oscillations of fourth order functional differential equations. (English) Zbl 1180.34064
Summary: We establish some sufficient conditions for the oscillations of all solutions of fourth-order functional differential equations
$\frac {d}{dt}\Bigg(a(t)\bigg( \frac{d^2}{dt^3}x(t)\bigg)^\alpha\Bigg)+ q(t)f(x[g(t)])=0$
and
$\frac {d}{dt}\Bigg(a(t)\bigg( \frac{d^2}{dt^3}x(t)\bigg)^\alpha\Bigg)= q(t)f(x[g(t)])+ p(t)h(x(t)])$
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