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A class of complete second order
linear differential equations

Author: Hirokazu Oka
Journal: Proc. Amer. Math. Soc. 124 (1996), 3143-3150
MSC (1991): Primary 42D05, 34G10
MathSciNet review: 1328367
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Abstract: This paper is concerned with a class of complete second order linear differential equations in a Banach space. We show the existence and uniqueness of classical solutions of

 \begin{equation}\tag {SE}\label {eq:SE} % \begin {cases} % u''(t) = A(t)u'(t) + B(t)u(t) + f(t) \ % \text {for $t \in [0,T]$} \\ % u(0) = x \ % \text {and} \ u'(0) = y. % \end {cases} % \end{equation}

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  • 1. G. Da Prato and E. Sinestrari, Differential operators with non dense domain, Ann. Scuola Norm. Sup. Pisa XIV (1987), 285--344. MR 89f:47062
  • 2. G. Da Prato and E. Sinestrari, Non autonomous evolution operators of hyperbolic type, Semigroup Forum 45 (1992), 302--321. MR 93h:34101
  • 3. R. Grimmer and J.H. Liu, Integrated semigroups and integrodifferential equations, Semigroup Forum 48 (1994), 79--95. MR 95f:47066
  • 4. T. Kato, Linear evolution equations of hyperbolic type, J. Fac. Sci. Univ. Tokyo, Sec. I 17 (1970), 241--258. MR 43:5347
  • 5. S.G. Krein, Linear Differential Equations in Banach Spaces, Translations of Math. Monographs, Vol. 29, Amer. Math. Soc., Providence, R I. 1971. MR 49:2548
  • 6. R. Nagel and E. Sinestrari, Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators. In: K.D. Bierstedt, A. Pietsch, W.M. Ruess, D. Vogt (eds.) : Functional Analysis, Proc. Essen Conference. Lect. Notes Pure Appl. Math. 150, Marcel Dekker (1994), 51--70. MR 94i:34121
  • 7. F. Neubrander, Well-posedness of higher order abstract Cauchy problems, Trans. Amer. Math. Soc. 295 (1986), 257--290. MR 88a:34087
  • 8. F. Neubrander, Integrated semigroups and their application to complete second order Cauchy problems, Semigroup Forum 38 (1989), 233--251. MR 89m:47038
  • 9. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,Springer-Verlag, New York, 1983. MR 85g:47061
  • 10. N. Tanaka, Semilinear equations in the hyperbolic case, Nonlinear Analysis 24 (1995), 773--788.

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Additional Information

Hirokazu Oka
Affiliation: School of Education, Department of Mathematics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-50, Japan
Address at time of publication: Ibaraki University, Faculty of Engineering, 12-1 Nakanarusawa 4 chome, Hitachi, Ibaraki, 316 Japan

Received by editor(s): January 17, 1995
Received by editor(s) in revised form: April 3, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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