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January  2002, 8(1): 39-54. doi: 10.3934/dcds.2002.8.39

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, Belgium
2. 

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, United States

Received  January 2001 Revised  May 2001 Published  October 2001

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.
Keywords: coincidence degree., Guiding functions, periodic solutions, bounded solutions.
Mathematics Subject Classification: 34C25, 34D4.
Citation: Jean Mawhin, James R. Ward Jr. Guiding-like functions for periodic or bounded solutions of ordinary differential equations. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 39-54. doi: 10.3934/dcds.2002.8.39
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