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Linear integro-differential equations in Banach spaces. (English) Zbl 0451.45014

MSC:
45N05Abstract integral equations, integral equations in abstract spaces
45J05Integro-ordinary differential equations
WorldCat.org
Full Text: Numdam EuDML
References:
[1] V. Barbu , Nonlinear Volterra equations in a Hilbert space , SIAM J. Math. Anal. , 6 ( 1975 ), pp. 728 - 741 . MR 377620 | Zbl 0322.45012 · Zbl 0322.45012 · doi:10.1137/0506064
[2] M.G. Crandall - S.-O. Londen - J.A. Nohel , An abstract nonlinear Volterra integrodifferential equation , J. Math. Anal. Appl. , 64 ( 1978 ), pp. 701 - 735 . MR 500052 | Zbl 0395.45023 · Zbl 0395.45023 · doi:10.1016/0022-247X(78)90014-8
[3] C. Dafermos , An abstract Volterra equation with applications to linear viscoelasticity , J. Diff. Eq. , 7 ( 1970 ), pp. 554 - 569 . MR 259670 | Zbl 0212.45302 · Zbl 0212.45302 · doi:10.1016/0022-0396(70)90101-4
[4] G. Da Prato - E. Giusti , Una caratterizzazione dei generatori di funzioni coseno astratte , Boll. U.M.I. , 3 ( 1967 ), pp. 1 - 6 . MR 240672 | Zbl 0186.47702 · Zbl 0186.47702 · eudml:195052
[5] G. Da Prato - M. Iannelli , Linear abstract integrodifferential equations of hyperbolic type in Hilbert spaces , Rend. Sem. Mat. Padova , 62 ( 1980 ), pp. 191 - 206 . Numdam | MR 582950 | Zbl 0451.45013 · Zbl 0451.45013 · numdam:RSMUP_1980__62__191_0 · eudml:107744
[6] A. Friedman - M. Shinbrot , Volterra integral equations in Banach spaces , Trans. A.M.S ., 126 ( 1967 ), pp. 131 - 179 . MR 206754 | Zbl 0147.12302 · Zbl 0147.12302 · doi:10.2307/1994417
[7] R.C. Grimmer - R. K. MILLER, Existence uniqueness and continuity for integral equations in Banach spaces , J. Math. Anal. Appl. , 57 ( 1977 ), pp. 429 - 447 . MR 440311 | Zbl 0354.45006 · Zbl 0354.45006 · doi:10.1016/0022-247X(77)90270-0
[8] S.-O. Londen , On an integrodifferential Volterra equation with a maximal monotone mapping , J. Diff. Eq. , 27 ( 1978 ), pp. 405 - 420 . MR 499976 | Zbl 0364.45003 · Zbl 0364.45003 · doi:10.1016/0022-0396(78)90060-8
[9] S.-O. Londen , An esistence result on a Volterra equation in a Banach space , Trans. A.M.S. , 235 ( 1978 ), pp. 285 - 304 . MR 473770 | Zbl 0376.45011 · Zbl 0376.45011 · doi:10.2307/1998220
[10] R.K. Miller , Volterra integral equations in a Banach space , Funk. Ekv. ,. 18 ( 1975 ), pp. 163 - 194 . Article | MR 410312 | Zbl 0326.45007 · Zbl 0326.45007 · http://minidml.mathdoc.fr/cgi-bin/location?id=00119695
[11] G.F. Webb , An abstract semilinear Volterra integrodifferential equation , Proc. A.M.S. , 69 ( 1978 ), pp. 225 - 260 . MR 467214 | Zbl 0388.45012 · Zbl 0388.45012 · doi:10.2307/2042608