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

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...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 346; pp. 183 - 192
Main Authors Yu, Xingchen, Lu, Shiping
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2019
Subjects
Liénard equation
Multiplicity result
Periodic solutions
Singularity
Upper and lower functions
Multiplicity result
Singularity
Periodic solutions
Liénard equation
Upper and lower functions
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.10.013