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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.

34K11Oscillation theory of functional-differential equations
Full Text: DOI
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[2] Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for second order dynamic equations. (2003) · Zbl 1043.34032
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