## Necessary and sufficient conditions for the oscillation of forced nonlinear second order differential equations with delayed argument.(English)Zbl 0884.34075

Under the assumption that $$a(t)$$ is nonnegative, there exists a bounded solution $$h(t)$$ of $h''(t)= g(t)\quad\text{and}\quad\phi(t)\leq t,\;\lim_{t\to\infty} \phi(t)=\infty,$ 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.

### MSC:

 34K11 Oscillation theory of functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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### References:

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