Grace, Said R.; Agarwal, Ravi P.; Pinelas, Sandra On the oscillations of fourth order functional differential equations. (English) Zbl 1180.34064 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 PDF BibTeX XML Cite \textit{S. R. Grace} et al., Commun. Appl. Anal. 13, No. 1, 93--103 (2009; Zbl 1180.34064)