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Necessary and sufficient conditions for boundedness and oscillation in the retarded Liénard equation. (English) Zbl 0855.34090

The retarded Liénard equation (1) \(x'' + f(x)x' + g(x(t - h)) = 0\) with continuous \(f\), \(g : \mathbb{R} \to \mathbb{R}\), \(h = \text{const} \geq 0\) is considered. Necessary and sufficient conditions of boundedness and oscillation of solutions to (1) are demonstrated. This result is compared with earlier ones obtained by Burton, Graef, Sansone, Conti, Villari for (1) with \(h = 0\).

MSC:

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