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On analytic structure of solutions to higher order abstract Cauchy problems
Author(s):
Yulia
Mishura;
Yuri
Tomilov
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1363-1370.
MSC (1991):
Primary 34G10, 47D09, 47A50
MathSciNet review:
1443162
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Abstract:
We prove the existence of entire solutions to some abstract higher order Cauchy problem for a dense subset of initial values.
References:
- 1.
- R. Beals, Semigroups and abstract Gevrey spaces, J. Funct. Anal. 10, (1972), 300-308. MR 50:14355
- 2.
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- 3.
- H. O. Fattorini, Ordinary differential equations in linear topological spaces I, J. of Diff. Eq. 5, (1969), 72-105. MR 43:3593
- 4.
- H. O. Fattorini, The abstract Goursat problem, Pacific. J. Math. 37, (1971), 51-83. MR 46:9793
- 5.
- Yu. I. Lyubich, The classical and local Laplace transform in the abstract Cauchy problem, Russian Math. Surveys 21, (1966), no. 3, 1-52. MR 33:7889
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- S. Nelson, R. Triggiani, Analytic properties of cosine operators, Proc. Amer. Math. Soc. 74, (1979), 101-104. MR 80h:47051
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- 8.
- W. Roth, Goursat problem for
, Indiana Univ. Math. J. 22, (1973), 779-788. MR 46:9568
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Additional Information:
Yulia
Mishura
Affiliation:
Department of Mathematics, Kiev University, 64 Vladimirskaya str., Kiev 252601, Ukraine
Email:
mishura@math.carrier.kiev.ua
Yuri
Tomilov
Affiliation:
Department of Mathematics, Kiev University, 64 Vladimirskaya str., Kiev 252601, Ukraine
Email:
tomilov@math.carrier.kiev.ua
DOI:
10.1090/S0002-9939-98-04068-4
PII:
S 0002-9939(98)04068-4
Keywords:
Abstract Cauchy problem,
entire solution
Received by editor(s):
November 13, 1995
Received by editor(s) in revised form:
October 14, 1996
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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