Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness

@article{349614,
   author = {Pavlačková, Martina and Taddei, Valentina},
   article_number = {1},
   doi = {http://dx.doi.org/10.5817/AM2023-1-99},
   keywords = {second-order differential inclusion; nonlocal conditions; Banach spaces; cosine family; approximation solvability method; mild solution},
   language = {eng},
   issn = {0044-8753},
   journal = {Archivum Mathematicum},
   title = {Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness},
   url = {https://emis.de/journals/AM/23-1/Pavlackova.pdf},
   volume = {59},
   year = {2023}
}

TY  - JOUR
ID  - 349614
AU  - Pavlačková, Martina - Taddei, Valentina
PY  - 2023
TI  - Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness
JF  - Archivum Mathematicum
VL  - 59
IS  - 1
SP  - 99-107
EP  - 99-107
SN  - 00448753
KW  - second-order differential inclusion
KW  - nonlocal conditions
KW  - Banach spaces
KW  - cosine family
KW  - approximation solvability method
KW  - mild solution
UR  - https://emis.de/journals/AM/23-1/Pavlackova.pdf
N2  - We study the existence of a mild solution to the nonlocal initial value problem for semilinear second-order differential inclusions in abstract spaces. The result is obtained by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables getting the result without any requirements for compactness of the right-hand side or of the cosine family generated by the linear operator.
ER  - 

PAVLAČKOVÁ, Martina and Valentina TADDEI. Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness. \textit{Archivum Mathematicum}. 2023, vol.~59, No~1, p.~99-107. ISSN~0044-8753. Available from: https://dx.doi.org/10.5817/AM2023-1-99.