2024
Bound Sets Approach to Impulsive Floquet Problems for Vector Second-Order Differential Inclusions
PAVLAČKOVÁ, Martina and Valentina TADDEIBasic information
Original name
Bound Sets Approach to Impulsive Floquet Problems for Vector Second-Order Differential Inclusions
Authors
PAVLAČKOVÁ, Martina (203 Czech Republic, belonging to the institution) and Valentina TADDEI
Edition
Differential Equations and Dynamical Systems, 2024, 0971-3514
Other information
Language
English
Type of outcome
Article in a journal
Field of Study
10102 Applied mathematics
Country of publisher
India
Confidentiality degree
is not subject to a state or trade secret
References:
Impact factor
Impact factor: 1.000 in 2022
Organization unit
Moravian Business College Olomouc
UT WoS
000737089900001
EID Scopus
2-s2.0-85122131203
Keywords in English
Impulsive Floquet problem; Upper-Carathéodory diferential inclusions; Bounding functions; Liénard type equation
Tags
Changed: 25/3/2025 13:30, Ing. Michaela Nováková
Abstract
V originále
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.