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Volumn 214, Issue 1, 2005, Pages 65-91

Strong solutions for differential equations in abstract spaces

Author keywords

Differential equations in locally convex spaces; Regularity theory; Strong solutions

Indexed keywords


EID: 18244386973     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.11.006     Document Type: Article
Times cited : (23)

References (37)
  • 1
    • 0001054041 scopus 로고
    • A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations
    • O. Arino S. Gautier J.P. Penot A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations Funkcial. Ekvac. 27 3 1984 273-279
    • (1984) Funkcial. Ekvac. , vol.27 , Issue.3 , pp. 273-279
    • Arino, O.1    Gautier, S.2    Penot, J.P.3
  • 2
    • 0038020299 scopus 로고
    • On Peano's theorem in locally convex spaces
    • K. Astala On Peano's theorem in locally convex spaces Stud. Math. 73 3 1982 213-223
    • (1982) Stud. Math. , vol.73 , Issue.3 , pp. 213-223
    • Astala, K.1
  • 3
    • 18244409276 scopus 로고    scopus 로고
    • A topological and geometric approach to fixed points results for sum of operators and applications
    • to appear
    • C.B. Barroso E.V. Teixeira A topological and geometric approach to fixed points results for sum of operators and applications, Nonlinear Anal., to appear.
    • Nonlinear Anal.
    • Barroso, C.B.1    Teixeira, E.V.2
  • 4
    • 0001912999 scopus 로고
    • On the existence of weak solutions of integral equations in Banach spaces
    • D. Bugajewski On the existence of weak solutions of integral equations in Banach spaces Comment. Math. Univ. Carolin. 35 1 1994 35-41
    • (1994) Comment. Math. Univ. Carolin. , vol.35 , Issue.1 , pp. 35-41
    • Bugajewski, D.1
  • 5
    • 18244368073 scopus 로고
    • An existence theorem for ordinary differential equations in Banach spaces
    • S. Chow J.D. Schuur An existence theorem for ordinary differential equations in Banach spaces Bull. Amer. Math. Soc. 77 1971 1018-1020
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 1018-1020
    • Chow, S.1    Schuur, J.D.2
  • 6
    • 0039332350 scopus 로고
    • Weak solutions of differential equations in Banach spaces
    • M. Cichoń Weak solutions of differential equations in Banach spaces Discuss. Math. Differential Incl. 15 1 1995 5-14
    • (1995) Discuss. Math. Differential Incl. , vol.15 , Issue.1 , pp. 5-14
    • Cichoń, M.1
  • 7
    • 0039332349 scopus 로고    scopus 로고
    • Existence theorem for the Hammerstein integral equation
    • M. Cichoń I. Kubiaczyk Existence theorem for the Hammerstein integral equation Discuss. Math. Differential Incl. 16 2 1996 171-177
    • (1996) Discuss. Math. Differential Incl. , vol.16 , Issue.2 , pp. 171-177
    • Cichoń, M.1    Kubiaczyk, I.2
  • 8
    • 0000950150 scopus 로고
    • On the existence of weak solutions of differential equations in nonreflexive Banach spaces
    • E. Cramer V. Lakshmikantham A.R. Mitchell On the existence of weak solutions of differential equations in nonreflexive Banach spaces Nonlinear Anal. 2 1978 169-177
    • (1978) Nonlinear Anal. , vol.2 , pp. 169-177
    • Cramer, E.1    Lakshmikantham, V.2    Mitchell, A.R.3
  • 9
    • 0001959149 scopus 로고
    • Deux exemples singuliers d'équations différentielles
    • J. Dieudonné Deux exemples singuliers d'équations différentielles, Acta. Scien. Math. (Szeged) 12 (1950) B38-40.
    • (1950) Acta. Scien. Math. (Szeged) , vol.12
    • Dieudonné, J.1
  • 10
    • 84968502635 scopus 로고
    • Weakly continuous nonlinear accretive operators in reflexive Banach spaces
    • W.E. Fitzgibbon Weakly continuous nonlinear accretive operators in reflexive Banach spaces Proc. Amer. Math. Soc. 41 1973 229-236
    • (1973) Proc. Amer. Math. Soc. , vol.41 , pp. 229-236
    • Fitzgibbon, W.E.1
  • 11
    • 0003107222 scopus 로고
    • Semilinear functional differential equations in Banach space
    • W.E. Fitzgibbon Semilinear functional differential equations in Banach space J. Differential Equations 29 1 1978 1-14
    • (1978) J. Differential Equations , vol.29 , Issue.1 , pp. 1-14
    • Fitzgibbon, W.E.1
  • 12
    • 0038020301 scopus 로고
    • Peano's theorem in Banach spaces
    • A.N. Godunov Peano's theorem in Banach spaces Functional. Anal. Appl. 9 1975 53-55
    • (1975) Functional. Anal. Appl. , vol.9 , pp. 53-55
    • Godunov, A.N.1
  • 13
    • 0037564275 scopus 로고    scopus 로고
    • Weak and strong solutions for differential equations in Banach spaces
    • A. Gomaa Weak and strong solutions for differential equations in Banach spaces Chaos Solitons Fractals 18 4 2003 687-692
    • (2003) Chaos Solitons Fractals , vol.18 , Issue.4 , pp. 687-692
    • Gomaa, A.1
  • 14
    • 0038696685 scopus 로고
    • On existence and uniqueness conditions for nonlinear ordinary differential equations in Banach spaces
    • S. Kato On existence and uniqueness conditions for nonlinear ordinary differential equations in Banach spaces Funkcial. Ekvac. 19 3 1976 239-245
    • (1976) Funkcial. Ekvac. , vol.19 , Issue.3 , pp. 239-245
    • Kato, S.1
  • 16
  • 18
    • 0038358484 scopus 로고
    • Peano's theorem is invalid for any infinite-dimensional Fréchet space
    • translation in Russian Acad. Sci. Sb. Math. 78(1) (1994) 211-214
    • S.G. Lobanov Peano's theorem is invalid for any infinite-dimensional Fréchet space, Mat. Sb. 184(2) (1993) 83-86 translation in Russian Acad. Sci. Sb. Math. 78(1) (1994) 211-214.
    • (1993) Mat. Sb. , vol.184 , Issue.2 , pp. 83-86
    • Lobanov, S.G.1
  • 20
    • 0039281681 scopus 로고
    • Weak compactness in L∞(μ,X)
    • G. Schlüchtermann Weak compactness in L∞(μ,X) J. Funct. Anal. 125 2 1994 379-388
    • (1994) J. Funct. Anal. , vol.125 , Issue.2 , pp. 379-388
    • Schlüchtermann, G.1
  • 21
    • 0010158451 scopus 로고
    • Existence theorem for weak solutions of ordinary differential equations in reflexive Banach spaces
    • A. Szep Existence theorem for weak solutions of ordinary differential equations in reflexive Banach spaces Studia Sci. Math. Hungar. 6 1971 197-203
    • (1971) Studia Sci. Math. Hungar. , vol.6 , pp. 197-203
    • Szep, A.1
  • 22
    • 0010686335 scopus 로고
    • Kneser's theorem for weak solutions of ordinary differential equations in reflexive Banach spaces
    • S. Szufla Kneser's theorem for weak solutions of ordinary differential equations in reflexive Banach spaces Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 5 1978 407-413
    • (1978) Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. , vol.26 , Issue.5 , pp. 407-413
    • Szufla, S.1
  • 23
    • 84911958777 scopus 로고    scopus 로고
    • A theory of differentiation in locally convex spaces
    • Memoirs of the American Mathematical Society no. 212
    • S. Yamamuro A theory of differentiation in locally convex spaces, Memoirs of the American Mathematical Society no. 212.
    • Yamamuro, S.1
  • 24
    • 0003021805 scopus 로고
    • A continuous differential equation in Hilbert space without existence
    • J.A. Yorke A continuous differential equation in Hilbert space without existence Funkcial. Ekv. 13 1970 19-21
    • (1970) Funkcial. Ekv. , vol.13 , pp. 19-21
    • Yorke, J.A.1
  • 25
    • 0013008597 scopus 로고    scopus 로고
    • Compact embeddings of vector-valued Sobolev and Besov spaces
    • H. Amann Compact embeddings of vector-valued Sobolev and Besov spaces Glas. Mat. Ser. III 35 1 2000 161-177
    • (2000) Glas. Mat. Ser. III , vol.35 , Issue.1 , pp. 161-177
    • Amann, H.1
  • 26
    • 0003087399 scopus 로고
    • Vector measures
    • Mathematical Surveys, No. 15, AMS, Providence, FI
    • J. Diestel Vector measures, Mathematical Surveys, No. 15, AMS, Providence, FI, 1977.
    • (1977) Mathematical Surveys
    • Diestel, J.1
  • 27
    • 18244364529 scopus 로고
    • Linear Operator, Interscience Publishers, Inc., New York, second printing
    • N. Dunford J. Schwartz Linear Operator, Interscience Publishers, Inc., New York, second printing, 1964.
    • (1964)
    • Dunford, N.1    Schwartz, J.2
  • 28
    • 38249034886 scopus 로고
    • Existence of generalized solutions for ordinary differential equations in Banach spaces
    • S.Z. Feng Existence of generalized solutions for ordinary differential equations in Banach spaces J. Math. Anal. Appl. 128 2 1987 405-412
    • (1987) J. Math. Anal. Appl. , vol.128 , Issue.2 , pp. 405-412
    • Feng, S.Z.1
  • 29
    • 18244365513 scopus 로고
    • Existence of solutions of differential equations in Banach space
    • W.J. Knight Existence of solutions of differential equations in Banach space Bull. Amer. Math. Soc. 80 1974 148-149
    • (1974) Bull. Amer. Math. Soc. , vol.80 , pp. 148-149
    • Knight, W.J.1
  • 30
    • 0042928312 scopus 로고
    • Existence of solutions for ordinary differential equations in Banach spaces
    • T.Y. Li Existence of solutions for ordinary differential equations in Banach spaces J. Differential Equations 18 1975 29-40
    • (1975) J. Differential Equations , vol.18 , pp. 29-40
    • Li, T.Y.1
  • 32
    • 18244397875 scopus 로고    scopus 로고
    • On the behaivor of weak convergence under nonlinearities and applications
    • to appear
    • D. Moreira E.V. Teixeira On the behaivor of weak convergence under nonlinearities and applications, Proc. Amer. Mat. Soc., to appear.
    • Proc. Amer. Mat. Soc.
    • Moreira, E.V.1    Teixeira, D.2
  • 33
    • 21344457989 scopus 로고    scopus 로고
    • Integral equations in reflexive Banach spaces and weak topologies
    • D. O'Regan Integral equations in reflexive Banach spaces and weak topologies Proc. Amer. Math. Soc. 124 2 1996 607-614
    • (1996) Proc. Amer. Math. Soc. , vol.124 , Issue.2 , pp. 607-614
    • O'Regan, D.1
  • 34
    • 0032221126 scopus 로고    scopus 로고
    • Operator equations in Banach spaces relative to the weak topology
    • D. O'regan Operator equations in Banach spaces relative to the weak topology Arch. Math. Basel 71 2 1998 123-136
    • (1998) Arch. Math. Basel , vol.71 , Issue.2 , pp. 123-136
    • O'regan, D.1
  • 35
    • 18244372380 scopus 로고    scopus 로고
    • A note on the existence of weak solutions to operator equations in Banach spaces
    • D. O'regan A note on the existence of weak solutions to operator equations in Banach spaces Dynam. Systems Appl. 8 1 1999 113-118
    • (1999) Dynam. Systems Appl. , vol.8 , Issue.1 , pp. 113-118
    • O'regan, D.1
  • 36
    • 0002061550 scopus 로고    scopus 로고
    • Weak solutions of ordinary differential equations in Banach spaces
    • D. O'regan Weak solutions of ordinary differential equations in Banach spaces Appl. Math. Lett. 12 1 1999 101-105
    • (1999) Appl. Math. Lett. , vol.12 , Issue.1 , pp. 101-105
    • O'regan, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.