메뉴 건너뛰기




Volumn 93, Issue 1, 1999, Pages 22-41

Well-posedness of differential-operator problems. II: The cauchy problem for complete second-order equations in banach spaces

(2)  Melnikova, I V a   Filinkov, A I a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 53149109724     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02365213     Document Type: Article
Times cited : (2)

References (67)
  • 1
    • 0004021335 scopus 로고
    • Springer-Verlag, Berlin-New York
    • K. Yosida, Functional Analysis, Springer-Verlag, Berlin-New York (1980).
    • (1980) Functional Analysis
    • Yosida, K.1
  • 3
    • 0009342028 scopus 로고
    • Differential equations in a Banach space
    • Itogi Nauki i Tekhniki, VINITI, Moscow
    • S. G. Krein and M. I. Kazan, "Differential equations in a Banach space," In: Progress in Science and Technology. Series on Math. Anal. Vol. 21, Itogi Nauki i Tekhniki, VINITI, Moscow (1983), pp. 130-232.
    • (1983) Progress in Science and Technology. Series on Math. Anal. , vol.21 , pp. 130-232
    • Krein, S.G.1    Kazan, M.I.2
  • 5
    • 53149099612 scopus 로고
    • Classification and well-posedness of the Cauchy problem for secondorder equations in a Banach space
    • I. V. Melnikova and A. I. Filinkov, "Classification and well-posedness of the Cauchy problem for secondorder equations in a Banach space," Dokl. Akad. Nauk SSSR, 276, 1066-1071 (1984);
    • (1984) Dokl. Akad. Nauk SSSR , vol.276 , pp. 1066-1071
    • Melnikova, I.V.1    Filinkov, A.I.2
  • 6
    • 53149089711 scopus 로고
    • English transl. in Sov. Math. Dokl., 29 (1984).
    • (1984) Sov. Math. Dokl. , vol.29
  • 7
    • 53149150870 scopus 로고
    • The family of M, N operator functions and second-order equations in Banach space
    • I. V. Melnikova, "The family of M, N operator functions and second-order equations in Banach space," Izv. Vuzov, Mat., No. 2, 45-52 (1985);
    • (1985) Izv. Vuzov, Mat. , Issue.2 , pp. 45-52
    • Melnikova, I.V.1
  • 8
    • 85034521463 scopus 로고    scopus 로고
    • English transl. in Sov. Math., 29, No. 2 (1985).
    • Sov. Math. , vol.29 , Issue.2 , pp. 1985
  • 9
    • 53149102329 scopus 로고
    • A theorem of Miyadera-Feller-Phillips-type for a complete second-order equation in a Banach space
    • I. V. Melnikova, "A theorem of Miyadera-Feller-Phillips-type for a complete second-order equation in a Banach space," Izv. Vuzov, Mat., No. 4, 34-40 (1985);
    • (1985) Izv. Vuzov, Mat. , Issue.4 , pp. 34-40
    • Melnikova, I.V.1
  • 10
    • 85034521463 scopus 로고    scopus 로고
    • English transl. in Sov. Math., 29, No. 4 (1985).
    • Sov. Math. , vol.29 , Issue.4 , pp. 1985
  • 11
    • 53149131234 scopus 로고
    • The connection between well-posedness of the Cauchy problen for an equation and for a system in a Banach space
    • I. V. Melnikova and A. I. Filinkov, "The connection between well-posedness of the Cauchy problen for an equation and for a system in a Banach space," Dokl. Akad. Nauk SSSR, 300, 280-284 (1988);
    • (1988) Dokl. Akad. Nauk SSSR , vol.300 , pp. 280-284
    • Melnikova, I.V.1    Filinkov, A.I.2
  • 12
    • 85034494783 scopus 로고    scopus 로고
    • English transl. in Sov. Math. Dokl., 37 (1988).
    • Sov. Math. Dokl. , vol.37 , pp. 1988
  • 13
    • 53149102328 scopus 로고
    • Classification with respect to boundary-value problems of a complete second-order equation in a Banach space
    • I. V. Melnikova and A. I. Filinkov, "Classification with respect to boundary-value problems of a complete second-order equation in a Banach space,"Izv. Vuzov, Mat., No. 6, 39-45 (1990);
    • (1990) Izv. Vuzov, Mat. , Issue.6 , pp. 39-45
    • Melnikova, I.V.1    Filinkov, A.I.2
  • 14
    • 85034514469 scopus 로고    scopus 로고
    • English transl. in Sov. Math., 34, No. 6 (1990).
    • Sov. Math. , vol.34 , Issue.6 , pp. 1990
  • 15
    • 53149117357 scopus 로고
    • The integrated family of M, TV-functions
    • I. V. Melnikova and A. I. Filinkov, "The integrated family of M, TV-functions," Dokl. Akad. Nauk, 326, 35-39 (1992);
    • (1992) Dokl. Akad. Nauk , vol.326 , pp. 35-39
    • Melnikova, I.V.1    Filinkov, A.I.2
  • 17
    • 21844524793 scopus 로고
    • Integrated semigroups and C-semigroups. Well-posedness and regularization of differential-operator problems
    • I. V. Melnikova and A. I. Filinkov, "Integrated semigroups and C-semigroups. Well-posedness and regularization of differential-operator problems," Usp. Mat. Nauk, 49, No. 6, 111-150 (1994);
    • (1994) Usp. Mat. Nauk , vol.49 , Issue.6 , pp. 111-150
    • Melnikova, I.V.1    Filinkov, A.I.2
  • 19
    • 0039531787 scopus 로고
    • Well-posedness of a degenerate Cauchy problem, in a Banach space
    • I. V. Melnikova and M. A. Alshansky, "Well-posedness of a degenerate Cauchy problem, in a Banach space," Dokl. Akad. Nauk, 336, No. 1, 17-24 (1994);
    • (1994) Dokl. Akad. Nauk , vol.336 , Issue.1 , pp. 17-24
    • Melnikova, I.V.1    Alshansky, M.A.2
  • 21
    • 0038848544 scopus 로고    scopus 로고
    • Well-posedness of the Cauchy problem in a Banach space: Regular and degenerate cases
    • Itogi Nauki i Tekhniki, Analysis-9, VINITI, Moscow
    • I. V. Melnikova and M. A. Alshansky, "Well-posedness of the Cauchy problem in a Banach space: regular and degenerate cases," Progress in Science and Technology. Series on Math. Anal., Vol. 21, Itogi Nauki i Tekhniki, Analysis-9, VINITI, Moscow (1996), 5-64;
    • (1996) Progress in Science and Technology. Series on Math. Anal. , vol.21 , pp. 5-64
    • Melnikova, I.V.1    Alshansky, M.A.2
  • 22
    • 85034514263 scopus 로고    scopus 로고
    • to appear.
    • English transl. in J. Math. Sci., to appear.
    • J. Math. Sci.
  • 23
    • 85034491769 scopus 로고
    • Well-posedness of differential-operator problem. I: The Cauchy problem in spaces of distributions
    • Itogi Nauki i Tekhniki, Analysis-9, VINITI, Moscow
    • I. V. Melnikova, "Well-posedness of differential-operator problem. I: the Cauchy problem in spaces of distributions," Progress in Science and Technology. Series on Math. Anal., Vol. 21, Itogi Nauki i Tekhniki, Analysis-9, VINITI, Moscow (1995).
    • (1995) Progress in Science and Technology. Series on Math. Anal. , vol.21
    • Melnikova, I.V.1
  • 24
    • 51649147034 scopus 로고
    • Vector valued Laplace transforms and Cauchy problems
    • W. Arendt, "Vector valued Laplace transforms and Cauchy problems," Israel J. Math., 59, 327-352 (1987).
    • (1987) Israel J. Math. , vol.59 , pp. 327-352
    • Arendt, W.1
  • 25
    • 0040870804 scopus 로고
    • Integrated solutions to implicit differential equations
    • W. Arendt and A. Favini, "Integrated solutions to implicit differential equations," Rend. Sem. Mat. Univ. Pol. Torino, 51, No. 4, 316-329 (1993).
    • (1993) Rend. Sem. Mat. Univ. Pol. Torino , vol.51 , Issue.4 , pp. 316-329
    • Arendt, W.1    Favini, A.2
  • 26
    • 0010002590 scopus 로고
    • Interpolation of semigroups and integrated semigroups
    • W. Arendt, F. Neubrander, and U. Schlotterbeck, "Interpolation of semigroups and integrated semigroups," Semigroup Forum, 45, 26-37 (1992).
    • (1992) Semigroup Forum , vol.45 , pp. 26-37
    • Arendt, W.1    Neubrander, F.2    Schlotterbeck, U.3
  • 27
    • 0040144773 scopus 로고
    • Existence for implicit differential equations in Banach spaces
    • V. Barby and A. Favini, "Existence for implicit differential equations in Banach spaces," Rend. Mat. Ace. Lincei, 9, No. 3, 203-215 (1992).
    • (1992) Rend. Mat. Ace. Lincei , vol.9 , Issue.3 , pp. 203-215
    • Barby, V.1    Favini, A.2
  • 28
    • 34250407282 scopus 로고
    • On exponential-cosine operator-valued functional equations
    • A. B. Buche, "On exponential-cosine operator-valued functional equations," Aequat. Math., 13, No. 3, 233-241 (1975).
    • (1975) Aequat. Math. , vol.13 , Issue.3 , pp. 233-241
    • Buche, A.B.1
  • 29
    • 0000455856 scopus 로고
    • The Cauchy problem and a generalization of the Hille-Yosida theorem
    • E. B. Davies and M. M. H. Pang, "The Cauchy problem and a generalization of the Hille-Yosida theorem," Proc. London Math. Soc., 55, No. 3, 181-208 (1987).
    • (1987) Proc. London Math. Soc. , vol.55 , Issue.3 , pp. 181-208
    • Davies, E.B.1    Pang, M.M.H.2
  • 30
    • 51249173616 scopus 로고
    • Integrated semigroups, C-semigroups, and the abstract Cauchy problem
    • R. deLaubenfels, "Integrated semigroups, C-semigroups, and the abstract Cauchy problem," Semigroup Forum, 41, 83-95 (1990).
    • (1990) Semigroup Forum , vol.41 , pp. 83-95
    • Delaubenfels, R.1
  • 32
    • 0003517384 scopus 로고
    • Addison-Wesley, Reading, Massachusetts
    • H. O. Fattorini, The Cauchy Problem, Addison-Wesley, Reading, Massachusetts (1983).
    • (1983) The Cauchy Problem
    • Fattorini, H.O.1
  • 34
    • 0001096743 scopus 로고
    • Ordinary differential equations in linear topological spaces, i
    • H. O. Fattorini, "Ordinary differential equations in linear topological spaces, I," J. Diff. Eq., 5, 72-105 (1969).
    • (1969) J. Diff. Eq. , vol.5 , pp. 72-105
    • Fattorini, H.O.1
  • 35
    • 0001096741 scopus 로고
    • Ordinary differential equations in linear topological spaces, II
    • H. O. Fattorini, "Ordinary differential equations in linear topological spaces, II," J. Diff. Eq., 6, 50-70 (1969).
    • (1969) J. Diff. Eq. , vol.6 , pp. 50-70
    • Fattorini, H.O.1
  • 36
    • 0011497552 scopus 로고
    • Extension and behavior at infinity of solutions of certain linear operational differential equations
    • H. O. Fattorini, "Extension and behavior at infinity of solutions of certain linear operational differential equations," Pacific J. Math., 33, 583-615 (1970).
    • (1970) Pacific J. Math. , vol.33 , pp. 583-615
    • Fattorini, H.O.1
  • 37
    • 25444518555 scopus 로고
    • Some remarks on second-order abstract Cauchy problems
    • H. O. Fattorini, " Some remarks on second-order abstract Cauchy problems," Funkc. Ekvacioj, 24, 331-344 (1981).
    • (1981) Funkc. Ekvacioj , vol.24 , pp. 331-344
    • Fattorini, H.O.1
  • 38
    • 51249175665 scopus 로고
    • Parabolicity of second differential order equations in Hubert space
    • A. Favini, "Parabolicity of second differential order equations in Hubert space," Semigroup Forum, 42, 303-312 (1991).
    • (1991) Semigroup Forum , vol.42 , pp. 303-312
    • Favini, A.1
  • 39
    • 0000010665 scopus 로고
    • Multivalued linear operators and degenerate evolution equations
    • A. Favini and A. Yagi, "Multivalued linear operators and degenerate evolution equations," Ann. Mat. Pura Appi, 4, 353-384 (1993).
    • (1993) Ann. Mat. Pura Appi , vol.4 , pp. 353-384
    • Favini, A.1    Yagi, A.2
  • 40
    • 0042302916 scopus 로고
    • Abstract second order differential equations with applications
    • A. Favini and A. Yagi, "Abstract second order differential equations with applications," Funkc. Ekvacioj, 38, 81-89 (1995).
    • (1995) Funkc. Ekvacioj , vol.38 , pp. 81-89
    • Favini, A.1    Yagi, A.2
  • 41
    • 0001742402 scopus 로고
    • Conditions for parabolicity of second-order abstract differential equations
    • A. Favini and E. Obrecht, "Conditions for parabolicity of second-order abstract differential equations," Diff. Int. Eg., 4, No. 5, 1005-1022 (1991).
    • (1991) Diff. Int. Eg. , vol.4 , Issue.5 , pp. 1005-1022
    • Favini, A.1    Obrecht, E.2
  • 42
    • 0014792497 scopus 로고
    • On a connection between first- And second-order differential equations in Banach spaces
    • J. A. Goldstein, "On a connection between first- and second-order differential equations in Banach spaces," J. Math. Anal. Appl., 30, 246-251 (1970).
    • (1970) J. Math. Anal. Appl. , vol.30 , pp. 246-251
    • Goldstein, J.A.1
  • 44
    • 34250141849 scopus 로고
    • Exponential-cosine operator-valued functional equations in the strong operator topology
    • S. Harshinder and H. L. Vasudeva, " Exponential-cosine operator-valued functional equations in the strong operator topology," Aequat. Math., 27, Nos. 1-2, 187-197 (1984).
    • (1984) Aequat. Math. , vol.27 , Issue.1-2 , pp. 187-197
    • Harshinder, S.1    Vasudeva, H.L.2
  • 45
    • 0000549509 scopus 로고
    • Integrated semigroups
    • H. Kellerman and M. Hieber, "Integrated semigroups," J. Fund. Anal., 84, 160-180 (1989).
    • (1989) J. Fund. Anal. , vol.84 , pp. 160-180
    • Kellerman, H.1    Hieber, M.2
  • 47
    • 84961475207 scopus 로고
    • General theory of ill-posed Cauchy problems
    • I. V. Melnikova, "General theory of ill-posed Cauchy problems," Inverse Problems, 3, No. 2, 149-171 (1995).
    • (1995) Inverse Problems , vol.3 , Issue.2 , pp. 149-171
    • Melnikova, I.V.1
  • 48
    • 85034509917 scopus 로고    scopus 로고
    • The regular and degenerate Cauchy problem for the complete second-order equation in a Danach space
    • to appear.
    • I. V. Melnikova, "The regular and degenerate Cauchy problem for the complete second-order equation in a Danach space," Stud. Math. (1996), to appear.
    • (1996) Stud. Math.
    • Melnikova, I.V.1
  • 49
    • 32944480644 scopus 로고
    • Cosine operator functions and abstract Cauchy problems
    • B. Nagy, "Cosine operator functions and abstract Cauchy problems," Period. Math. Hung., 7, No. 3, 15-18 (1976).
    • (1976) Period. Math. Hung. , vol.7 , Issue.3 , pp. 15-18
    • Nagy, B.1
  • 50
    • 84968505402 scopus 로고
    • Well-posedness of higher order abstract Cauchy problems
    • F. Neubrander, "Well-posedness of higher order abstract Cauchy problems," Trans. Amer. Math. Soc., 295, No. 1, 257-290 (1986).
    • (1986) Trans. Amer. Math. Soc. , vol.295 , Issue.1 , pp. 257-290
    • Neubrander, F.1
  • 51
    • 84972562394 scopus 로고
    • Integrated semigroups and their application to the abstract Cauchy problem
    • F. Neubrander, "Integrated semigroups and their application to the abstract Cauchy problem," Pacific J. Math., 135, 111-155 (1988).
    • (1988) Pacific J. Math. , vol.135 , pp. 111-155
    • Neubrander, F.1
  • 52
    • 51249175702 scopus 로고
    • Integrated semigroups and their application to complete second order Cauchy problems
    • F. Neubrander, "Integrated semigroups and their application to complete second order Cauchy problems," Semigroup Forum, 38, 233-251 (1989).
    • (1989) Semigroup Forum , vol.38 , pp. 233-251
    • Neubrander, F.1
  • 54
    • 0001410978 scopus 로고
    • Existence and uniqueness of solutions of second order nonlinear differential equations
    • J. T, Sandefur, "Existence and uniqueness of solutions of second order nonlinear differential equations," J. Math. Anal. Appl., 14, No. 3, 477-486 (1983).
    • (1983) J. Math. Anal. Appl. , vol.14 , Issue.3 , pp. 477-486
    • Sandefur, J.T.1
  • 55
    • 0001947072 scopus 로고
    • Cosine operator functions
    • M. Sova, "Cosine operator functions," Rozpr. Math., 49, 1-47 (1966).
    • (1966) Rozpr. Math. , vol.49 , pp. 1-47
    • Sova, M.1
  • 56
    • 0043175161 scopus 로고
    • Probleme de Cauchy pour equations hyperboliques opérationnelles a coefficients constants non-bornés
    • M. Sova, "Probleme de Cauchy pour equations hyperboliques opérationnelles a coefficients constants non-bornés," Ann. Scuola Norm. Sup. Pisa. Sci. Fis. Mat., 22, No. 1, 67-100 (1968).
    • (1968) Ann. Scuola Norm. Sup. Pisa. Sci. Fis. Mat. , vol.22 , Issue.1 , pp. 67-100
    • Sova, M.1
  • 57
    • 27544493840 scopus 로고
    • Linear differential equations in Banach spaces
    • M. Sova, "Linear differential equations in Banach spaces," Rozpr. CSAV MPV, 85, No. 6, 1-150 (1975).
    • (1975) Rozpr. CSAV MPV , vol.85 , Issue.6 , pp. 1-150
    • Sova, M.1
  • 58
    • 84972526385 scopus 로고
    • Exponentially bounded C-semigroups and integrated semigroups
    • N. Tanaka and I. Miyadera, "Exponentially bounded C-semigroups and integrated semigroups," Tokyo J. Math., 12, 99-115 (1989).
    • (1989) Tokyo J. Math. , vol.12 , pp. 99-115
    • Tanaka, N.1    Miyadera, I.2
  • 59
    • 34250278681 scopus 로고
    • Cosine families and abstract nonlinear second-order differential equations
    • G. C. Travis and G. F. Webb, "Cosine families and abstract nonlinear second-order differential equations," Ada Math. Acad. Sci. Hung., 32, Nos. 3-4, 75-96 (1978).
    • (1978) Ada Math. Acad. Sci. Hung. , vol.32 , Issue.3-4 , pp. 75-96
    • Travis, G.C.1    Webb, G.F.2
  • 60
    • 84973998961 scopus 로고
    • On complete second order linear differential equations in Banach spaces
    • T. Xio and J. Liang, "On complete second order linear differential equations in Banach spaces," Pacific J. Math., 142, No. 1, 175-195 (1990).
    • (1990) Pacific J. Math. , vol.142 , Issue.1 , pp. 175-195
    • Xio, T.1    Liang, J.2
  • 61
    • 84968519572 scopus 로고
    • A note on the propagators of second order linear differential equations in Hubert space
    • T. Xio and J. Liang, "A note on the propagators of second order linear differential equations in Hubert space," Proc. Amer. Math. Soc., 113, No. 3, 663-667 (1991).
    • (1991) Proc. Amer. Math. Soc. , vol.113 , Issue.3 , pp. 663-667
    • Xio, T.1    Liang, J.2
  • 62
    • 51249164851 scopus 로고
    • Analyticity of the propagators of second order linear differential equations in Banach spaces
    • T. Xio and J. Liang, "Analyticity of the propagators of second order linear differential equations in Banach spaces," Semigroup Forum, 44, 356-363 (1992).
    • (1992) Semigroup Forum , vol.44 , pp. 356-363
    • Xio, T.1    Liang, J.2
  • 63
    • 38249011547 scopus 로고
    • Complete second order linear differential equations with almost periodic solutions
    • T. Xio and J. Liang, "Complete second order linear differential equations with almost periodic solutions," J. MaUi. Anal. Appl., 163, No. 1, 136-146 (1992).
    • (1992) J. MaUi. Anal. Appl. , vol.163 , Issue.1 , pp. 136-146
    • Xio, T.1    Liang, J.2
  • 64
    • 84972566453 scopus 로고
    • Generation theorems of semigroups for multivalued linear operators
    • A.Yagi, "Generation theorems of semigroups for multivalued linear operators," Osaka J. Math., 28, 385-410 (1991).
    • (1991) Osaka J. Math. , vol.28 , pp. 385-410
    • Yagi, A.1
  • 66
    • 0040238216 scopus 로고
    • A Hille-Yosida theorem for the higher order abstract Cauchy problem
    • Q. Zheng, "A Hille-Yosida theorem for the higher order abstract Cauchy problem," Bull. London Math. Soc., 24, 531-539 (1992).
    • (1992) Bull. London Math. Soc. , vol.24 , pp. 531-539
    • Zheng, Q.1
  • 67
    • 34147212513 scopus 로고
    • Strongly continuous M, JV-families of bounded operators
    • Q. Zheng, "Strongly continuous M, JV-families of bounded operators," Integr. Equat, Oper. Theory, 19, 106-119 (1994).
    • (1994) Integr. Equat, Oper. Theory , vol.19 , pp. 106-119
    • Zheng, Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.