메뉴 건너뛰기




Volumn 68, Issue 2, 2010, Pages 207-227

Bounded Mild Solutions for Semilinear Integro Differential Equations in Banach Spaces

Author keywords

bounded mild solutions; Linear and semilinear integro differential equations; regularized operator families

Indexed keywords


EID: 77956917525     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-010-1799-2     Document Type: Article
Times cited : (74)

References (45)
  • 1
    • 0006795644 scopus 로고    scopus 로고
    • Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain
    • Amir B., Maniar L.: Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain. Ann. Math. Blaise Pascal 6(1), 1-11 (1999).
    • (1999) Ann. Math. Blaise Pascal , vol.6 , Issue.1 , pp. 1-11
    • Amir, B.1    Maniar, L.2
  • 3
    • 53949107192 scopus 로고    scopus 로고
    • Almost automorphic mild solutions to fractional differential equations
    • Araya D., Lizama C.: Almost automorphic mild solutions to fractional differential equations. Nonlinear Anal. 69(11), 3692-3705 (2008).
    • (2008) Nonlinear Anal. , vol.69 , Issue.11 , pp. 3692-3705
    • Araya, D.1    Lizama, C.2
  • 4
    • 77955449562 scopus 로고    scopus 로고
    • Superposition operators between various almost periodic function spaces and applications
    • Blot J., Cieutat P., N'Guérékata G. M., Pennequin D.: Superposition operators between various almost periodic function spaces and applications. Commun. Math. Anal. 6(1), 42-70 (2009).
    • (2009) Commun. Math. Anal. , vol.6 , Issue.1 , pp. 42-70
    • Blot, J.1    Cieutat, P.2    N'Guérékata, G.M.3    Pennequin, D.4
  • 5
    • 0001074459 scopus 로고
    • A new approach to almost periodicity
    • Bochner S.: A new approach to almost periodicity. Proc. Natl. Acad. Sci. USA 48, 2039-2043 (1962).
    • (1962) Proc. Natl. Acad. Sci. USA , vol.48 , pp. 2039-2043
    • Bochner, S.1
  • 6
    • 34250584790 scopus 로고
    • Zur theorie der fast periodischen funktionen. (German) I. Eine verallgemeinerung der theorie der fourierreihen
    • Bohr H.: Zur theorie der fast periodischen funktionen. (German) I. Eine verallgemeinerung der theorie der fourierreihen. Acta Math. 45(1), 29-127 (1925).
    • (1925) Acta Math. , vol.45 , Issue.1 , pp. 29-127
    • Bohr, H.1
  • 7
    • 9244234347 scopus 로고    scopus 로고
    • On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces
    • Bugajewski D., N'Guérékata G. M.: On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces. Nonlinear Anal. 59, 1333-1345 (2004).
    • (2004) Nonlinear Anal. , vol.59 , pp. 1333-1345
    • Bugajewski, D.1    N'Guérékata, G.M.2
  • 8
    • 3042586902 scopus 로고
    • Existence and regularity results for an integral equation with infinite delay in a Banach space
    • Clément Ph., Da Prato G.: Existence and regularity results for an integral equation with infinite delay in a Banach space. Integr. Equ. Oper. Theory 11, 480-500 (1988).
    • (1988) Integr. Equ. Oper. Theory , vol.11 , pp. 480-500
    • Clément, P.1    da Prato, G.2
  • 9
    • 0000522482 scopus 로고
    • Equipresence and constitutive equation for rigid heat conductors
    • Coleman B. D., Gurtin M. E.: Equipresence and constitutive equation for rigid heat conductors. Z. Angew. Math. Phys. 18, 199-208 (1967).
    • (1967) Z. Angew. Math. Phys. , vol.18 , pp. 199-208
    • Coleman, B.D.1    Gurtin, M.E.2
  • 10
    • 53249152135 scopus 로고    scopus 로고
    • Almost automorphic solutions to a class of semilinear fractional differential equations
    • Cuevas C., Lizama C.: Almost automorphic solutions to a class of semilinear fractional differential equations. Appl. Math. Lett. 21, 1315-1319 (2008).
    • (2008) Appl. Math. Lett. , vol.21 , pp. 1315-1319
    • Cuevas, C.1    Lizama, C.2
  • 11
    • 0001629395 scopus 로고
    • Asymptotic stability in viscoelasticity
    • Dafermos C. M.: Asymptotic stability in viscoelasticity. Arch. Rational Mech. Anal. 37, 297-308 (1970).
    • (1970) Arch. Rational Mech. Anal. , vol.37 , pp. 297-308
    • Dafermos, C.M.1
  • 12
    • 0001029815 scopus 로고
    • An abstract Volterra equation with applications to linear viscoelasticity
    • Dafermos C. M.: An abstract Volterra equation with applications to linear viscoelasticity. J. Differ. Equ. 7, 554-569 (1970).
    • (1970) J. Differ. Equ. , vol.7 , pp. 554-569
    • Dafermos, C.M.1
  • 13
    • 3042672654 scopus 로고
    • Periodic solutions for linear integrodifferential equations with infinite delay in Banach spaces. Differential Equations in Banach spaces
    • Da Prato G., Lunardi A.: Periodic solutions for linear integrodifferential equations with infinite delay in Banach spaces. Differential Equations in Banach spaces. Lect. Notes Math. 1223, 49-60 (1985).
    • (1985) Lect. Notes Math. , vol.1223 , pp. 49-60
    • da Prato, G.1    Lunardi, A.2
  • 14
    • 0040662280 scopus 로고
    • Solvability on the real line of a class of linear Volterra integrodifferential equations of parabolic type
    • Da Prato G., Lunardi A.: Solvability on the real line of a class of linear Volterra integrodifferential equations of parabolic type. Ann. Math. Pura Appl. 4, 67-117 (1988).
    • (1988) Ann. Math. Pura Appl. , vol.4 , pp. 67-117
    • da Prato, G.1    Lunardi, A.2
  • 15
    • 29444443899 scopus 로고
    • The asymptotically periodic behavior of the solutions of some linear functional equations
    • De Bruijn N. G.: The asymptotically periodic behavior of the solutions of some linear functional equations. Am. J. Math. 71, 313-330 (1949).
    • (1949) Am. J. Math. , vol.71 , pp. 313-330
    • de Bruijn, N.G.1
  • 16
    • 33751114130 scopus 로고    scopus 로고
    • Weighted pseudo almost automorphic functions and applications
    • Diagana T.: weighted pseudo almost automorphic functions and applications. C. R. Acad. Sci. Paris Ser. I 343, 643-646 (2006).
    • (2006) C. R. Acad. Sci. Paris Ser. I , vol.343 , pp. 643-646
    • Diagana, T.1
  • 17
    • 64849090450 scopus 로고    scopus 로고
    • Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations
    • Diagana T., Hernández E., Dos Santos J. P. C.: Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations. Nonlinear Anal. 71, 248-257 (2009).
    • (2009) Nonlinear Anal. , vol.71 , pp. 248-257
    • Diagana, T.1    Hernández, E.2    Dos Santos, J.P.C.3
  • 18
    • 44649086371 scopus 로고    scopus 로고
    • Almost automorphic mild solutions to some partial neutral functional-differential equations and applications
    • Diagana T., Henríquez H., Hernández E.: Almost automorphic mild solutions to some partial neutral functional-differential equations and applications. Nonlinear Anal. 69(5-6), 1485-1493 (2008).
    • (2008) Nonlinear Anal. , vol.69 , Issue.5-6 , pp. 1485-1493
    • Diagana, T.1    Henríquez, H.2    Hernández, E.3
  • 19
    • 34548847768 scopus 로고    scopus 로고
    • Asymptotically almost automorphic solutions for some integro-differential equations with nonlocal conditions
    • Ding H.-S., Liang J., Xiao T.-J.: Asymptotically almost automorphic solutions for some integro-differential equations with nonlocal conditions. J. Math. Anal. Appl. 338(1), 141-151 (2008).
    • (2008) J. Math. Anal. Appl. , vol.338 , Issue.1 , pp. 141-151
    • Ding, H.-S.1    Liang, J.2    Xiao, T.-J.3
  • 20
    • 0035802859 scopus 로고    scopus 로고
    • Asymptotic behaviour of a semilinear viscoelastic beam model
    • Fašangová E., Prüss J.: Asymptotic behaviour of a semilinear viscoelastic beam model. Arch. Math. (Basel) 77, 488-497 (2001).
    • (2001) Arch. Math. (Basel) , vol.77 , pp. 488-497
    • Fašangová, E.1    Prüss, J.2
  • 21
    • 84972573844 scopus 로고
    • Almost automorphic and almost periodic solutions which minimize functionals
    • Fink A. M.: Almost automorphic and almost periodic solutions which minimize functionals. Tôhoku Math. J. 20(2), 323-332 (1968).
    • (1968) Tôhoku Math. J. , vol.20 , Issue.2 , pp. 323-332
    • Fink, A.M.1
  • 22
    • 0010991321 scopus 로고
    • Les fonctions asymptotiquement presque-periodiques continues (French)
    • Fréchet M.: Les fonctions asymptotiquement presque-periodiques continues (French). C. R. Acad. Sci. Paris 213, 520-522 (1941).
    • (1941) C. R. Acad. Sci. Paris , vol.213 , pp. 520-522
    • Fréchet, M.1
  • 23
    • 33745148633 scopus 로고    scopus 로고
    • Massera-type theorem and asymptotically periodic logistic equations
    • Gao H., Wang K., Wei F., Ding X.: Massera-type theorem and asymptotically periodic logistic equations. Nonlinear Anal. Real World Appl. 7, 1268-1283 (2006).
    • (2006) Nonlinear Anal. Real World Appl. , vol.7 , pp. 1268-1283
    • Gao, H.1    Wang, K.2    Wei, F.3    Ding, X.4
  • 25
    • 72149112210 scopus 로고    scopus 로고
    • Compact almost periodic solutions to integral equations with infinite delay
    • Henríquez H. R., Lizama C.: Compact almost periodic solutions to integral equations with infinite delay. Nonlinear Anal. 71, 6029-6037 (2009).
    • (2009) Nonlinear Anal. , vol.71 , pp. 6029-6037
    • Henríquez, H.R.1    Lizama, C.2
  • 26
    • 71849098853 scopus 로고    scopus 로고
    • Existence of S-asymptotically ω-periodic solutions for abstract neutral equations
    • Henríquez H. R., Pierri M., Táboas P.: Existence of S-asymptotically ω-periodic solutions for abstract neutral equations. Bull. Aust. Math. Soc. 78, 365-382 (2008).
    • (2008) Bull. Aust. Math. Soc. , vol.78 , pp. 365-382
    • Henríquez, H.R.1    Pierri, M.2    Táboas, P.3
  • 27
    • 41949083295 scopus 로고    scopus 로고
    • On S-asymptotically ω-periodic functions on Banach spaces and applications
    • Henríquez H. R., Pierri M., Táboas P.: On S-asymptotically ω-periodic functions on Banach spaces and applications. J. Math. Anal. Appl. 343(2), 1119-1130 (2008).
    • (2008) J. Math. Anal. Appl. , vol.343 , Issue.2 , pp. 1119-1130
    • Henríquez, H.R.1    Pierri, M.2    Táboas, P.3
  • 28
    • 77956898107 scopus 로고    scopus 로고
    • Levitan, B. M., Zhikov, V. V.: Almost Periodic Functions and Differential Equations. Moscow University House, Moscow (1978) (English Translation by Cambridge University Press, 1982).
  • 29
    • 0035869881 scopus 로고    scopus 로고
    • Composition of pseudo almost periodic functions and semilinear differential equations
    • Li H., Huang F., Li J.: Composition of pseudo almost periodic functions and semilinear differential equations. J. Math. Anal. Appl. 255, 436-446 (2001).
    • (2001) J. Math. Anal. Appl. , vol.255 , pp. 436-446
    • Li, H.1    Huang, F.2    Li, J.3
  • 30
    • 38049089402 scopus 로고    scopus 로고
    • Composition of pseudo almost automorphic and asymptotically almost automorphic functions
    • Liang J., Zhang J., Xiao T. J.: Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J. Math. Anal. Appl. 340(2), 1493-1499 (2008).
    • (2008) J. Math. Anal. Appl. , vol.340 , Issue.2 , pp. 1493-1499
    • Liang, J.1    Zhang, J.2    Xiao, T.J.3
  • 31
    • 0034652891 scopus 로고    scopus 로고
    • Regularized solutions for abstract Volterra equations
    • Lizama C.: Regularized solutions for abstract Volterra equations. J. Math. Anal. Appl. 243, 278-292 (2000).
    • (2000) J. Math. Anal. Appl. , vol.243 , pp. 278-292
    • Lizama, C.1
  • 32
    • 77956916192 scopus 로고    scopus 로고
    • Mophou, G. M., N'Guérékata, G. M.: On some classes of almost automorphic functions and applications to fractional differential equations (2010, to appear).
  • 35
    • 9244237996 scopus 로고
    • Quelques remarques sur les fonctions asymptotiquement presque automorphes (French)
    • N'Guérékata G. M.: Quelques remarques sur les fonctions asymptotiquement presque automorphes (French). Ann. Sci. Math. Quebec 7(2), 185-191 (1983).
    • (1983) Ann. Sci. Math. Quebec , vol.7 , Issue.2 , pp. 185-191
    • N'Guérékata, G.M.1
  • 36
    • 39749121694 scopus 로고    scopus 로고
    • Comments on almost automorphic and almost periodic functions in Banach spaces
    • N'Guérékata G. M.: Comments on almost automorphic and almost periodic functions in Banach spaces. Far East J. Math. Sci. (FJMS) 17(3), 337-344 (2005).
    • (2005) Far East J. Math. Sci. (FJMS) , vol.17 , Issue.3 , pp. 337-344
    • N'Guérékata, G.M.1
  • 37
    • 17144453621 scopus 로고    scopus 로고
    • Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations
    • N'Guérékata G. M.: Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations. Semigroup Forum 69, 80-86 (2004).
    • (2004) Semigroup Forum , vol.69 , pp. 80-86
    • N'Guérékata, G.M.1
  • 38
    • 33750506477 scopus 로고    scopus 로고
    • A spectral countability condition for almost automorphy of solutions of differential equations
    • Nguyen V. M., Naito T., N'Guérékata G. M.: A spectral countability condition for almost automorphy of solutions of differential equations. Proc. Am. Math. Soc. 134, 3257-3266 (2006).
    • (2006) Proc. Am. Math. Soc. , vol.134 , pp. 3257-3266
    • Nguyen, V.M.1    Naito, T.2    N'Guérékata, G.M.3
  • 39
    • 0008849603 scopus 로고
    • On heat conduction in materials with memory
    • Nunziato J. W.: On heat conduction in materials with memory. Q. Appl. Math. 29, 187-304 (1971).
    • (1971) Q. Appl. Math. , vol.29 , pp. 187-304
    • Nunziato, J.W.1
  • 40
    • 77956894344 scopus 로고    scopus 로고
    • Prüss, J.: Evolutionary integral equations and applications. In: Monographs in Mathematics, vol. 87. Birkhäuser, Boston (1993).
  • 41
    • 77956929767 scopus 로고    scopus 로고
    • Renardy, M., Hrusa, W. J., Nohel, J. A.: Mathematical problems in viscoelasticity. In: Pitman Monographs Pure Applied Mathematics, vol. 35. Longman Sci. Tech., Harlow, Essex (1988).
  • 42
    • 0242463498 scopus 로고
    • Existence in the large for a semilinear integrodifferential equation with infinite delay
    • Sforza D.: Existence in the large for a semilinear integrodifferential equation with infinite delay. J. Differ. Equ. 120, 289-303 (1995).
    • (1995) J. Differ. Equ. , vol.120 , pp. 289-303
    • Sforza, D.1
  • 43
    • 42249086144 scopus 로고    scopus 로고
    • Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces
    • Xiao T. J., Liang J., Zhang J.: Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces. Semigroup Forum 76(3), 518-524 (2008).
    • (2008) Semigroup Forum , vol.76 , Issue.3 , pp. 518-524
    • Xiao, T.J.1    Liang, J.2    Zhang, J.3
  • 44
    • 0034276937 scopus 로고    scopus 로고
    • Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument
    • Yuan R.: Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument. Nonlinear Anal. 41(7-8), 871-890 (2000).
    • (2000) Nonlinear Anal. , vol.41 , Issue.7-8 , pp. 871-890
    • Yuan, R.1
  • 45
    • 84966211078 scopus 로고
    • Integration of vector-valued pseudo-almost periodic functions
    • Zhang C. Y.: Integration of vector-valued pseudo-almost periodic functions. Proc. Am. Math. Soc. 121(1), 167-174 (1994).
    • (1994) Proc. Am. Math. Soc. , vol.121 , Issue.1 , pp. 167-174
    • Zhang, C.Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.