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Oscillation theorems for fourth order functional differential equations. (English) Zbl 1188.34085
By means of the oscillation of three related first-order functional differential equations, the authors investigate the oscillatory behavior of all solutions of the fourth-order functional differential equations
\[ \frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha})+q(t)f(x[g(t)])=0 \] and
\[ \frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha}) =q(t)f(x[g(t)]) +p(t)h(x[\sigma(t)]) \] in the case when \(\int ^{\infty } a^{-1/\alpha} (s)ds<\infty \). Examples and remarks are also included to illustrate the applicability of the obtained results.

MSC:
34K11 Oscillation theory of functional-differential equations
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