Necessary and sufficient conditions for boundedness and oscillation in the retarded Liénard equation
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 \(h = 0\).
scientific article; zbMATH DE number 897965