(ω,Q)-periodic mild solutions for a class of semilinear abstract differential equations and applications to Hopfield-type neural network model

In this paper, we investigate the existence and uniqueness of ( ω , Q ) -periodic mild solutions for the following problem x ′ ( t ) = A x ( t ) + f ( t , x ( t ) ) , t ∈ R , on a Banach space X . Here, A is a closed linear operator which generates an exponentially stable C 0 -semigroup and the nonl...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2023-04, Vol.74 (2), Article 60
Main Authors: Alvarez, E., Díaz, S., Grau, R.
Format: Article
Language:English
Subjects:
Banach spaces
Differential equations
Engineering
Linear operators
Mathematical Methods in Physics
Neural networks
Operators (mathematics)
Theoretical and Applied Mechanics
Uniqueness
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Summary:In this paper, we investigate the existence and uniqueness of ( ω , Q ) -periodic mild solutions for the following problem x ′ ( t ) = A x ( t ) + f ( t , x ( t ) ) , t ∈ R , on a Banach space X . Here, A is a closed linear operator which generates an exponentially stable C 0 -semigroup and the nonlinearity f satisfies suitable properties. The approaches are based on the well-known Banach contraction principle. In addition, a sufficient criterion is established for the existence and uniqueness of ( ω , Q ) -periodic mild solutions to the Hopfield-type neural network model.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-023-01943-9