Periodic solutions for indefinite singular equations with applications to the weak case

2017/07/14 by Manuel Zamora, Zamora, Manuel, José Godoy +1
Mathematics · #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1707.04513

openalex publication_date 2017/07/14 · openalex created_date 2017/07/21 · openalex updated_date 2026/07/28

Abstract

As a consequence of the main result of this paper efficient conditions guaranteeing the existence of a T-periodic solution to the second order differential equation u"=(h(t))/(u^λ) are established. Here, h∈ L(ℝ/Tℤ) is a piecewise-constant sign-changing function where the non-linear term presents a weak singularity at 0 (i.e. λ∈ (0,1)).

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