Resumen de Multiple Positive Periodic Solutions to Minkowski-Curvature Equations with a Singularity of Attractive Type

Zhibo Cheng, Ci Kong, Chenyang Xia

• Using Leray–Schauder degree theory, we investigate the existence and multiplicity of positive T -periodic solutions to Minkowski-curvature equations with a singularity of attractive type u √ 1 − u2 + f (u)u + ϕ(t)um + r(t) uμ = s, where f ∈ C((0, +∞), R), ϕ ∈ C(R, R) and r ∈ C(R, (0, +∞)) are T -periodic functions, m and μ are two positive constants and 0 < m ≤ 1, s ∈ R is a parameter.

  Based on a new method to construct upper and lower functions and some properties of Leray–Schauder degree, a multiplicity result of Ambrosetti-Prodi type is established.