Bound Sets Approach to Impulsive Floquet Problems for Vector Second‑Order Diferential Inclusions

@article{349563,
   author = {Pavlačková, Martina and Taddei, Valentina},
   article_number = {1},
   doi = {http://dx.doi.org/10.1007/s12591-021-00586-4},
   keywords = {Impulsive Floquet problem; Upper-Carathéodory diferential inclusions; Bounding functions; Liénard type equation},
   language = {eng},
   issn = {0971-3514},
   journal = {Differential Equations and Dynamical Systems},
   title = {Bound Sets Approach to Impulsive Floquet Problems for Vector Second‑Order Diferential Inclusions},
   url = {https://link.springer.com/article/10.1007/s12591-021-00586-4},
   volume = {30},
   year = {2022}
}

TY  - JOUR
ID  - 349563
AU  - Pavlačková, Martina - Taddei, Valentina
PY  - 2022
TI  - Bound Sets Approach to Impulsive Floquet Problems for Vector Second‑Order Diferential Inclusions
JF  - Differential Equations and Dynamical Systems
VL  - 30
IS  - 1
SP  - 1-21
EP  - 1-21
SN  - 09713514
KW  - Impulsive Floquet problem
KW  - Upper-Carathéodory diferential inclusions
KW  - Bounding functions
KW  - Liénard type equation
UR  - https://link.springer.com/article/10.1007/s12591-021-00586-4
N2  - In this paper, the existence and the localization of a solution of an impulsive vector multivalued second-order Floquet boundary value problem are investigated. The method used in the paper is based on the combination of a fixed point index technique with bound sets approach. At first, problems with upper-Carathéodory right-hand sides are investigated and it is shown afterwards how can the conditions be simplified in more regular case of upper semi-continuous right hand side. In this more regular case, the conditions ensuring the existence and the localization of a solution are put directly on the boundary of the considered bound set. This strict localization of the sufficient conditions is very significant since it allows some solutions to escape from the set of candidate solutions. In both cases, the C1 -bounding functions with locally Lipschitzian gradients are considered at first and it is shown afterwards how the conditions change in case of C2 -bounding functions. The paper concludes with an application of obtained results to Liénard-type equations and inclusions and the comparisons of our conclusions with the few results related to impulsive periodic and antiperiodic Liénard equations are obtained.
ER  - 

PAVLAČKOVÁ, Martina and Valentina TADDEI. Bound Sets Approach to Impulsive Floquet Problems for Vector Second‑Order Diferential Inclusions. \textit{Differential Equations and Dynamical Systems}. 2022, vol.~30, No~1, p.~1-21. ISSN~0971-3514. Available from: https://dx.doi.org/10.1007/s12591-021-00586-4.