Periodic solutions for indefinite singular perturbations of the relativistic acceleration
Published online by Cambridge University Press: 22 June 2018
Abstract
Using the Leray–Schauder degree, we study the existence of solutions for the following periodic differential equation with relativistic acceleration and singular nonlinearity:
where μ > 1 and the weight h: [0, T] → ℝ is a continuous sign-changing function. There are no a priori estimates on the set of positive solutions (a condition used in general to apply the Leray–Schauder degree), and we prove that no solution of the equation appears on the boundary of an unbounded open set during the deformation to an autonomous problem.
Keywords
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 4 , August 2018 , pp. 703 - 712
- Copyright
- Copyright © Royal Society of Edinburgh 2018
Footnotes
Present address: Departamento de Matemàticas, Universidad de Oviedo, Calle Federico García Lorca 18, 33007 Oviedo, Spain ([email protected]).
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