Asymptotic behavior for a linear Volterra integral equation in Hilbert space
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Published in | Journal of Differential Equations Vol. 23; no. 2; pp. 270 - 284 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.01.1977
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Author | Wheeler, Robert L Miller, Richard K |
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Author_xml | – sequence: 1 givenname: Richard K surname: Miller fullname: Miller, Richard K organization: Mathematics Department, Iowa State University, Ames, Iowa 50010 U.S.A – sequence: 2 givenname: Robert L surname: Wheeler fullname: Wheeler, Robert L organization: Mathematics Department, University of Missouri at Columbia, Columbia, Missouri 65201 U.S.A |
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Cites_doi | 10.1137/0506060 10.1016/0022-0396(74)90090-4 10.1090/S0002-9947-1967-0206754-7 10.1007/BF00251609 10.1137/0506046 10.1016/0022-247X(72)90240-5 10.1016/0022-247X(72)90276-4 10.2307/2373715 10.1016/0022-247X(75)90072-4 10.1016/0022-247X(72)90258-2 10.1090/S0002-9947-1972-0293355-X 10.1016/0022-247X(76)90067-6 |
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References | Miller (BIB10) 1975; 18 Hannsgen (BIB3) 1975; 6 Miller, Nohel (BIB11) 1975; 6 Friedman, Shinbrot (BIB2) 1967; 126 Taylor (BIB13) 1958 Miller (BIB9) 1974; 15 Jordan, Wheeler (BIB6) 1976; 55 Jordan, Wheeler (BIB5) 1976; 57 Dafermos (BIB1) 1970; 37 Levin, Shea, Levin, Shea, Levin, Shea (BIB7) 1972; 37 Shea, Wainger (BIB12) 1975; 97 Titchmarsh (BIB14) 1948 Jordan, Wheeler (BIB4) 1975; 52 MacCamy, Wong (BIB8) 1972; 164 Levin (10.1016/0022-0396(77)90130-9_BIB7_1) 1972; 37 MacCamy (10.1016/0022-0396(77)90130-9_BIB8) 1972; 164 Taylor (10.1016/0022-0396(77)90130-9_BIB13) 1958 Jordan (10.1016/0022-0396(77)90130-9_BIB4) 1975; 52 Levin (10.1016/0022-0396(77)90130-9_BIB7_3) 1972; 37 Dafermos (10.1016/0022-0396(77)90130-9_BIB1) 1970; 37 Levin (10.1016/0022-0396(77)90130-9_BIB7_2) 1972; 37 Miller (10.1016/0022-0396(77)90130-9_BIB9) 1974; 15 Jordan (10.1016/0022-0396(77)90130-9_BIB5) 1976; 57 Hannsgen (10.1016/0022-0396(77)90130-9_BIB3) 1975; 6 Jordan (10.1016/0022-0396(77)90130-9_BIB6) 1976; 55 Shea (10.1016/0022-0396(77)90130-9_BIB12) 1975; 97 Miller (10.1016/0022-0396(77)90130-9_BIB10) 1975; 18 Friedman (10.1016/0022-0396(77)90130-9_BIB2) 1967; 126 Miller (10.1016/0022-0396(77)90130-9_BIB11) 1975; 6 Titchmarsh (10.1016/0022-0396(77)90130-9_BIB14) 1948 |
References_xml | – volume: 57 start-page: 109 year: 1976 end-page: 114 ident: BIB5 article-title: A generalization of the Wiener-Lévy theorem applicable to some Volterra equations publication-title: Proc. Amer. Math. Soc. contributor: fullname: Wheeler – volume: 164 start-page: 1 year: 1972 end-page: 37 ident: BIB8 article-title: Stability theorems for some functional equations publication-title: Trans. Amer. Math. Soc. contributor: fullname: Wong – volume: 6 start-page: 506 year: 1975 end-page: 522 ident: BIB11 article-title: A stable manifold theorem for a system of Volterra integro-differential equations publication-title: SIAM J. Math. Anal. contributor: fullname: Nohel – volume: 55 start-page: 596 year: 1976 end-page: 615 ident: BIB6 article-title: Asymptotic behavior of unbounded solutions of linear Volterra integral equations publication-title: J. Math. Anal. Appl. contributor: fullname: Wheeler – volume: 126 start-page: 131 year: 1967 end-page: 179 ident: BIB2 article-title: Volterra integral equations in Banach space publication-title: Trans. Amer. Math. Soc. contributor: fullname: Shinbrot – volume: 15 start-page: 129 year: 1974 end-page: 157 ident: BIB9 article-title: Structure of solutions of unstable linear Volterra integrodifferential equations publication-title: J. Differential Equations contributor: fullname: Miller – year: 1958 ident: BIB13 article-title: Introduction to Functional Analysis contributor: fullname: Taylor – volume: 52 start-page: 454 year: 1975 end-page: 464 ident: BIB4 article-title: Linear integral equations with asymptotically almost periodic solutions publication-title: J. Math. Anal. Appl. contributor: fullname: Wheeler – volume: 37 start-page: 297 year: 1970 end-page: 308 ident: BIB1 article-title: Asymptotic stability in viscoelasticity publication-title: Arch. Rational Mech. Anal. contributor: fullname: Dafermos – volume: 97 start-page: 312 year: 1975 end-page: 343 ident: BIB12 article-title: Variants of the Wiener-Lévy theorem, with applications to stability problems for some Volterra integral equations publication-title: Amer. J. Math. contributor: fullname: Wainger – year: 1948 ident: BIB14 article-title: Introduction to the Theory of Fourier Integrals contributor: fullname: Titchmarsh – volume: 6 start-page: 689 year: 1975 end-page: 697 ident: BIB3 article-title: Uniform boundedness in a class of Volterra equations publication-title: SIAM J. Math. Anal. contributor: fullname: Hannsgen – volume: 37 start-page: 42 year: 1972 end-page: 82 ident: BIB7 article-title: On the asymptotic behavior of the bounded solutions of some integral equations. I publication-title: J. Math. Anal. Appl. contributor: fullname: Shea – volume: 18 start-page: 163 year: 1975 end-page: 193 ident: BIB10 article-title: Volterra integral equations in a Banach space publication-title: Funckcial. Ekvac. contributor: fullname: Miller – volume: 6 start-page: 689 year: 1975 ident: 10.1016/0022-0396(77)90130-9_BIB3 article-title: Uniform boundedness in a class of Volterra equations publication-title: SIAM J. Math. Anal. doi: 10.1137/0506060 contributor: fullname: Hannsgen – volume: 15 start-page: 129 year: 1974 ident: 10.1016/0022-0396(77)90130-9_BIB9 article-title: Structure of solutions of unstable linear Volterra integrodifferential equations publication-title: J. Differential Equations doi: 10.1016/0022-0396(74)90090-4 contributor: fullname: Miller – volume: 18 start-page: 163 year: 1975 ident: 10.1016/0022-0396(77)90130-9_BIB10 article-title: Volterra integral equations in a Banach space publication-title: Funckcial. Ekvac. contributor: fullname: Miller – volume: 126 start-page: 131 year: 1967 ident: 10.1016/0022-0396(77)90130-9_BIB2 article-title: Volterra integral equations in Banach space publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1967-0206754-7 contributor: fullname: Friedman – volume: 37 start-page: 297 year: 1970 ident: 10.1016/0022-0396(77)90130-9_BIB1 article-title: Asymptotic stability in viscoelasticity publication-title: Arch. Rational Mech. Anal. doi: 10.1007/BF00251609 contributor: fullname: Dafermos – volume: 6 start-page: 506 year: 1975 ident: 10.1016/0022-0396(77)90130-9_BIB11 article-title: A stable manifold theorem for a system of Volterra integro-differential equations publication-title: SIAM J. Math. Anal. doi: 10.1137/0506046 contributor: fullname: Miller – volume: 37 start-page: 537 year: 1972 ident: 10.1016/0022-0396(77)90130-9_BIB7_3 article-title: On the asymptotic behavior of the bounded solutions of some integral equations. III publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(72)90240-5 contributor: fullname: Levin – year: 1948 ident: 10.1016/0022-0396(77)90130-9_BIB14 contributor: fullname: Titchmarsh – volume: 37 start-page: 288 year: 1972 ident: 10.1016/0022-0396(77)90130-9_BIB7_2 article-title: On the asymptotic behavior of the bounded solutions of some integral equations. II publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(72)90276-4 contributor: fullname: Levin – volume: 97 start-page: 312 year: 1975 ident: 10.1016/0022-0396(77)90130-9_BIB12 article-title: Variants of the Wiener-Lévy theorem, with applications to stability problems for some Volterra integral equations publication-title: Amer. J. Math. doi: 10.2307/2373715 contributor: fullname: Shea – volume: 52 start-page: 454 year: 1975 ident: 10.1016/0022-0396(77)90130-9_BIB4 article-title: Linear integral equations with asymptotically almost periodic solutions publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(75)90072-4 contributor: fullname: Jordan – volume: 37 start-page: 42 year: 1972 ident: 10.1016/0022-0396(77)90130-9_BIB7_1 article-title: On the asymptotic behavior of the bounded solutions of some integral equations. I publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(72)90258-2 contributor: fullname: Levin – year: 1958 ident: 10.1016/0022-0396(77)90130-9_BIB13 contributor: fullname: Taylor – volume: 57 start-page: 109 year: 1976 ident: 10.1016/0022-0396(77)90130-9_BIB5 article-title: A generalization of the Wiener-Lévy theorem applicable to some Volterra equations contributor: fullname: Jordan – volume: 164 start-page: 1 year: 1972 ident: 10.1016/0022-0396(77)90130-9_BIB8 article-title: Stability theorems for some functional equations publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1972-0293355-X contributor: fullname: MacCamy – volume: 55 start-page: 596 year: 1976 ident: 10.1016/0022-0396(77)90130-9_BIB6 article-title: Asymptotic behavior of unbounded solutions of linear Volterra integral equations publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(76)90067-6 contributor: fullname: Jordan |
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