Guiding-like functions for periodic or bounded solutions of ordinary differential equations

Jean Mawhin; James R. Ward Jr

doi:10.3934/dcds.2002.8.39

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2002, Volume 8, Issue 1: 39-54. Doi: 10.3934/dcds.2002.8.39

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Guiding-like functions for periodic or bounded solutions of ordinary differential equations

Jean Mawhin^1, and
James R. Ward Jr^2,

1.
Institut Mathématique Pure et Appliquée, Université Catholique de Louvain, B-1348 Louvain-la-Neuve
2.
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294

Received: December 31, 2000

Revised: April 30, 2001

Published: December 2001

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Abstract

We state and prove some extensions of the fundamental theorem of the method of guiding functions for periodic and for bounded solutions of ordinary differential systems. Those results unify and generalize previous results of Krasnosel'skii, Perov, Mawhin, Walter and Gossez.

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Mathematics Subject Classification: 34C25, 34D40.

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