Da Prato, G.; Iannelli, M. Linear integro-differential equations in Banach spaces. (English) Zbl 0451.45014 Rend. Sem. Mat. Univ. Padova 62, 207-219 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 51 Documents MSC: 45N05 Abstract integral equations, integral equations in abstract spaces 45J05 Integro-ordinary differential equations Keywords:closed operator; existence; Banach space PDF BibTeX XML Cite \textit{G. Da Prato} and \textit{M. Iannelli}, Rend. Semin. Mat. Univ. Padova 62, 207--219 (1980; Zbl 0451.45014) 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 · minidml.mathdoc.fr [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.