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

Martina Pavlačková; Valentina Taddei

Archivum Mathematicum (2023)

  • Issue: 1, page 99-107
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Pavlačková, Martina, and Taddei, Valentina. "Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness." Archivum Mathematicum (2023): 99-107. <http://eudml.org/doc/298975>.

@article{Pavlačková2023,
abstract = {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.},
author = {Pavlačková, Martina, Taddei, Valentina},
journal = {Archivum Mathematicum},
keywords = {second-order differential inclusion; nonlocal conditions; Banach spaces; cosine family; approximation solvability method; mild solution},
language = {eng},
number = {1},
pages = {99-107},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness},
url = {http://eudml.org/doc/298975},
year = {2023},
}

TY - JOUR
AU - Pavlačková, Martina
AU - Taddei, Valentina
TI - Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 1
SP - 99
EP - 107
AB - 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.
LA - eng
KW - second-order differential inclusion; nonlocal conditions; Banach spaces; cosine family; approximation solvability method; mild solution
UR - http://eudml.org/doc/298975
ER -

References

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