On the abstract Cauchy problem in Fréchet spaces

Authors:
Hernán R. Henríquez and Eduardo A. Hernández

Journal:
Proc. Amer. Math. Soc. **115** (1992), 353-360

MSC:
Primary 47D03; Secondary 34G10, 47D06, 47D09

DOI:
https://doi.org/10.1090/S0002-9939-1992-1081092-1

MathSciNet review:
1081092

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a linear operator in a Fréchet space with the resolvent defined for all . In this note we prove that both the first and the second order abstract Cauchy problems associated to are well posed on certain maximal subspaces of . Our results extend those of Kantorovitz [5] and Cioranescu [2].

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1081092-1

Keywords:
Abstact Cauchy problem,
semigroup of operators,
cosine function of operators

Article copyright:
© Copyright 1992
American Mathematical Society