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Boundedness of solutions for a class of Liénard equations with a deviating argument

✍ Scribed by Bingwen Liu; Lihong Huang

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
149 KB
Volume
21
Category
Article
ISSN
0893-9659

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✦ Synopsis

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 derivatives to be bounded, which substantially extend and improve some important results from the literature.

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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 solutio