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Zbl 0884.34075
Nasr, A.H.
Necessary and sufficient conditions for the oscillation of forced nonlinear second order differential equations with delayed argument.
(English)
[J] J. Math. Anal. Appl. 212, No.1, 51-59 (1997). ISSN 0022-247X

Under the assumption that $a(t)$ is nonnegative, there exists a bounded solution $h(t)$ of $$h''(t)= g(t)\quad\text{and}\quad\phi(t)\le t,\ \lim_{t\to\infty} \phi(t)=\infty,$$ necessary conditions for equation $x''(t)+ a(t)|x(\phi(t))|^\nu\cdot \text{sgn }x(\phi(t))= g(t)$ to be oscillatory in the sublinear and the superlinear cases are established and when $h(t)$ has special properties, these conditions are also sufficient.
[W.Šeda (Bratislava)]
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: forced Emden-Fowler equation with delayed argument; oscillatory equation

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