A multiplicity result for periodic solutions of Liénard equations with an attractive singularity

Xingchen Yu and Shiping Lu

Applied Mathematics and Computation, 2019, vol. 346, issue C, 183-192

Abstract: A periodic problem of Ambrosetti–Prodi type is studied in this paper for the Liénard equation with a singularity of attractive typex″+f(x)x′+φ(t)xm+r(t)xμ=s,where f:(0,+∞)→R is continuous, r:R→(0,+∞) and φ: R → R are continuous with T−periodicity in the t variable, 0 < m ≤ 1, μ > 0, s ∈ R are constants. By using the method of upper and lower functions as well as some properties of topological degree, we obtain a new multiplicity result on the existence of periodic solutions for the equation.

Keywords: Liénard equation; Periodic solutions; Singularity; Upper and lower functions; Multiplicity result (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:183-192

DOI: 10.1016/j.amc.2018.10.013

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