A general result to the existence of a periodic solution to an indefinite equation with a weak singularity
type: Item
instance of: scholarly article
title: A general result to the existence of a periodic solution to an indefinite equation with a weak singularity
zbMATH Open document ID: 1447.34044
author: José Godoy
author: Manuel Zamora
published in: Journal of Dynamics and Differential Equations
publication date: 2019-04-25T00:00:00Z
review text: The paper investigates the existence of \(T\)-periodic solutions for the singular equation \[ u'' = \frac{h(t)}{u^\lambda}, \qquad u \in \mathbb{R}, \] where \(h(t)\) is a \(T\)-periodic integrable function with \(\int_0^T h(t)\,dt < 0\) and \(\lambda \in (0,1)\) (the so-called weak singularity case). A quite general result is first proved, by the use of Leray-Schauder degree theory, assuming that the weight function \(h(t)\) satisfies a rather technical condition, related to its oscillatory and symmetry properties. Some corollary are later provided, in the cases when \(h(t)\) is piecewise constant and piecewise affine.
reviewed by: Alberto Boscaggin
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7047674
zbMATH Keywords: singular differential equations
zbMATH Keywords: weak-indefinite singularity
zbMATH Keywords: periodic solutions
zbMATH Keywords: degree theory
zbMATH Keywords: Leray-Schauder continuation theorem
MaRDI profile type: Publication
full work available at URL: s10884-018-9704-9
OpenAlex ID: W2891566177
Wikidata QID: Q115383444
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DOI: 10.1007/S10884-018-9704-9
description: scientific article; zbMATH DE number 7047674