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

• Zhibo Cheng ^[1] ; Ci Kong ^[1] ; Chenyang Xia ^[1]
  1. [1] Henan Polytechnic University

     Henan Polytechnic University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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.

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