J 2022

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

PAVLAČKOVÁ, Martina and Valentina TADDEI

Basic information

Original name

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

Authors

PAVLAČKOVÁ, Martina (203 Czech Republic, belonging to the institution) and Valentina TADDEI

Edition

Differential Equations and Dynamical Systems, 2022, 0971-3514

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10102 Applied mathematics

Country of publisher

India

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Organization unit

Moravian Business College Olomouc

DOI

http://dx.doi.org/10.1007/s12591-021-00586-4

UT WoS

000737089900001

Keywords in English

Impulsive Floquet problem; Upper-Carathéodory diferential inclusions; Bounding functions; Liénard type equation

Tags

RIV2023
Změněno: 17/2/2023 10:36, 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.
Displayed: 31/10/2024 21:07