Mild solutions of second-order semilinear impulsive differential inclusions in Banach spaces
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Mild solutions of second-order semilinear impulsive differential inclusions in Banach spaces
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
O - Projekt operacniho programu
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
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Volume of the periodical
10
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
25
Pages from-to
1-25
UT code for WoS article
000761402300001
EID of the result in the Scopus database
2-s2.0-85125441598