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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F26867184%3A_____%2F22%3AN0000005" target="_blank" >RIV/26867184:_____/22:N0000005 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s12591-021-00586-4" target="_blank" >https://link.springer.com/article/10.1007/s12591-021-00586-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s12591-021-00586-4" target="_blank" >10.1007/s12591-021-00586-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

N - Vyzkumna aktivita podporovana z neverejnych zdroju

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Differential Equations and Dynamical Systems

ISSN

0971-3514

e-ISSN

—

Svazek periodika

30

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

IN - Indická republika

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

000737089900001

EID výsledku v databázi Scopus

2-s2.0-85122131203