Mild solutions of second-order semilinear impulsive differential inclusions in Banach spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F26867184%3A_____%2F22%3AN0000004" target="_blank" >RIV/26867184:_____/22:N0000004 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2227-7390/10/4/672" target="_blank" >https://www.mdpi.com/2227-7390/10/4/672</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math10040672" target="_blank" >10.3390/math10040672</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mild solutions of second-order semilinear impulsive differential inclusions in Banach spaces

Popis výsledku v původním jazyce

In this paper, the existence of a mild solution to the Cauchy problem for impulsive semilinear second-order differential inclusion in a Banach space is investigated in the case when the nonlinear term also depends on the first derivative. This purpose is achieved by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables obtaining the result under easily verifiable and not restrictive conditions on the impulsive terms, the cosine family generated by the linear operator and the right-hand side while avoiding any requirement for compactness. Firstly, the problems without impulses are investigated, and then their solutions are glued together to construct the solution to the impulsive problem step by step. The paper concludes with an application of the obtained results to the generalized telegraph equation with a Balakrishnan–Taylor-type damping term.

Název v anglickém jazyce

Mild solutions of second-order semilinear impulsive differential inclusions in Banach spaces

Popis výsledku anglicky

In this paper, the existence of a mild solution to the Cauchy problem for impulsive semilinear second-order differential inclusion in a Banach space is investigated in the case when the nonlinear term also depends on the first derivative. This purpose is achieved by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables obtaining the result under easily verifiable and not restrictive conditions on the impulsive terms, the cosine family generated by the linear operator and the right-hand side while avoiding any requirement for compactness. Firstly, the problems without impulses are investigated, and then their solutions are glued together to construct the solution to the impulsive problem step by step. The paper concludes with an application of the obtained results to the generalized telegraph equation with a Balakrishnan–Taylor-type damping term.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

25

Strana od-do

1-25

Kód UT WoS článku

000761402300001

EID výsledku v databázi Scopus

2-s2.0-85125441598