Mathematica Bohemica, Vol. 144, No. 4, pp. 373-392, 2019


Bound sets and two-point boundary value problems for second order differential systems

Jean Mawhin, Katarzyna Szymańska-Dębowska

Received February 7, 2019.   Published online June 24, 2019.

Abstract:  The solvability of second order differential systems with the classical separated or periodic boundary conditions is considered. The proofs use special classes of curvature bound sets or bound sets together with the simplest version of the Leray-Schauder continuation theorem. The special cases where the bound set is a ball, a parallelotope or a bounded convex set are considered.
Keywords:  two-point boundary value problem; curvature bound set; Leray-Schauder theorem; Bernstein-Hartman condition
Classification MSC:  34B15, 47H11


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Affiliations:   Jean Mawhin, Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, chemin du Cyclotron, 2, 1348 Louvain-la-Neuve, Belgium, e-mail: jean.mawhin@uclouvain.be; Katarzyna Szymańska-Dębowska, Institute of Mathematics, Lodz University of Technology, ul. Wólczańska 215, 90-924 Lódź, Poland, e-mail: katarzyna.szymanska-debowska@p.lodz.pl


 
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