Degree, quaternions and periodic solutions. (22nd February 2021)

• Record Type: Journal Article
• Authors: Mawhin, Jean
• Is Part Of: Philosophical transactions. Volume 379:Number 2191(2021)
• Publication Date: 2021-02-22
• Subjects: Brouwer degree -- coincidence degree -- quaternionic equations -- periodic solutions; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2019.0378
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : The paper computes the Brouwer degree of some classes of homogeneous polynomials defined on quaternions and applies the results, together with a continuation theorem of coincidence degree theory, to the existence and multiplicity of periodic solutions of a class of systems of quaternionic valued ordinary differential equations. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.