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.


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