Well posedness for evolution inclusions

K. Balachandran and A. Anguraj

International Journal of Stochastic Analysis, 1994, vol. 7, 1-8

Abstract:

We prove the existence of a continuous selection of the multivalued map φ → Φ ( φ ) which is the set of all mild solutions of the evolution inclusion x ( t ) ∈ A x ( t ) + F ( t , x ( t ) ) + ∫ 0 t h ( t − s ) g ( x ( s ) ) d s x ( 0 ) = φ . Here F is a multivalued map, Lipschitzian with respect to x , and A is the infinitesimal generator of a C 0 -semigroup.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:615767

DOI: 10.1155/S1048953394000419

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