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

摘要

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.