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

Grace, Said R.; Agarwal, Ravi P.; Pavani, Raffaella; Thandapani, E.

Appl. Math. Comput. 202, No. 1, 102-112 (2008).

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

Keywords:

functional differential equation; oscillation; nonoscillation; comparison

References:

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