On the Floquet problem for second-order Marchaud differential systems

Solutions in a given set of the Floquet boundary value problem are investigated for second-order Marchaud systems. The methods used involve a fixed point index technique developed by ourselves earlier with a bound sets approach. Since the related bounding (Liapunov-like) functions are strictly local...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-03, Vol.351 (1), p.360-372
Main Authors: Andres, Jan, Kožušníková, Martina, Malaguti, Luisa
Format: Article
Language:English
Subjects:
Bounding functions
Exact sciences and technology
Global analysis, analysis on manifolds
Marchaud differential inclusions
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Solutions in a given set
Topological methods
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Vector second-order Floquet problem
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Summary:Solutions in a given set of the Floquet boundary value problem are investigated for second-order Marchaud systems. The methods used involve a fixed point index technique developed by ourselves earlier with a bound sets approach. Since the related bounding (Liapunov-like) functions are strictly localized on the boundaries of parameter sets of candidate solutions, some trajectories are allowed to escape from these sets. The main existence and localization theorem is illustrated by two examples for periodic and anti-periodic problems.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.10.028