On the oscillations of fourth order functional differential equations. (English) Zbl 1180.34064

Grace, Said R.; Agarwal, Ravi P.; Pinelas, Sandra

Commun. Appl. Anal. 13, No. 1, 93-103 (2009).

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