Mild Solutions of Second-Order Semilinear Impulsive Differential Inclusions in Banach Spaces

Martina Pavlačková and Valentina Taddei
Additional contact information
Martina Pavlačková: Department of Informatics and Mathematics, Moravian Business College Olomouc, tř. Kosmonautů 1288/1, 77900 Olomouc, Czech Republic
Valentina Taddei: Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via G. Amendola, 2-pad. Morselli, 42122 Reggio Emilia, Italy

Mathematics, 2022, vol. 10, issue 4, 1-25

Abstract: 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.

Keywords: second-order Cauchy problem; Banach spaces; cosine family; approximation solvability method; mild solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/4/672/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/4/672/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:4:p:672-:d:754753

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().