Consider the Liénard equation with a deviating argument where f, g 1 and g 2 are continuous functions on R = (-∞, +∞), τ (t) ≥ 0 is a bounded continuous function on R, and e(t) is a bounded continuous function on R + = [0, +∞). We obtain some new sufficient conditions for all solutions and their de
Boundedness of solutions for a class of retarded Liénard equation
✍ Scribed by Bingwen Liu; Lihong Huang
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 194 KB
- Volume
- 286
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
Consider the retarded Liénard equation
where h is a nonnegative constant, f 1 , f 2 , and g are continuous functions on R = (-∞, +∞), and e(t) is a continuous function on R + = [0, +∞). We obtain some new sufficient conditions, as well as some new necessary and sufficient conditions for all solutions and their derivatives to be bounded, which substantially extend and improve some important results in the literature.
📜 SIMILAR VOLUMES
Consider the retarded Lienard equation xЉ q f x xЈ q g x t y h s 0, where f, g: R ª R are continuous and h G 0. Using Liapunov's direct method, we give necessary and sufficient conditions to ensure boundedness and oscillation of all solutions and their derivatives.
Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of T-periodic solutions for a Liénard equations with delay. An illustrative example is provided to demonstrate that the results in this paper hold under weaker conditions than