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On the Floquet problem for second-order Marchaud differential systems |
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| Authors: | Jan Andres Martina Ko?ušníková Luisa Malaguti |
| Institution: | a Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hej?ín, Czech Republic b Department of Engineering Sciences and Methods, University of Modena and Reggio Emilia, Via G. Amendola, 2-pad. Morselli, I-42100 Reggio Emilia, Italy |
| Abstract: | 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. |
| Keywords: | Vector second-order Floquet problem Marchaud differential inclusions Topological methods Bounding functions Solutions in a given set |
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