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 \(h = 0\).
Reviewer: T.Dłotko (Katowice)
MSC:
34K11 | Oscillation theory of functional-differential equations |
34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |