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Periodic solutions for a second-order differential equation with indefinite weak singularity

Published online by Cambridge University Press:  15 January 2019

José Godoy
Affiliation:
Departamento de Matemática, Grupo de investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile ([email protected]; [email protected])
Manuel Zamora
Affiliation:
Departamento de Matemática, Grupo de investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile ([email protected]; [email protected])

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

$${u}^{\prime \prime} = \displaystyle{{h(t)} \over {u^\lambda }}$$
are established. Here, hL(ℝ/Tℤ) is a piecewise-constant sign-changing function and the non-linear term presents a weak singularity at 0 (i.e. λ ∈ (0, 1)).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019 

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