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Volumn 28, Issue 12, 1997, Pages 1955-1976

Some spectral theory for nonlinear operators

Author keywords

Lipschitz operator; Measure of noncompactness; Nonlinear operator; Quasi bounded operator; Resolvent; Spectrum; bounded operator

Indexed keywords

BIFURCATION (MATHEMATICS); CALCULATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

EID: 0031165102     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00040-5     Document Type: Article
Times cited : (21)

References (35)
  • 1
    • 0042525974 scopus 로고
    • On the nonlinear spectrum of Furi and Vignoli
    • BHATT, S. R. and BHATT, S. J., On the nonlinear spectrum of Furi and Vignoli. Math. Today, 1984, 2, 49-64.
    • (1984) Math. Today , vol.2 , pp. 49-64
    • Bhatt, S.R.1    Bhatt, S.J.2
  • 2
    • 0001541411 scopus 로고
    • Contributions to the spectral theory for nonlinear operators in Banach spaces
    • FURI, M., MARTELLI, M. and VIGNOLI, A., Contributions to the spectral theory for nonlinear operators in Banach spaces. Ann. Mat. Pura Appl., 1978, 118, 229-294.
    • (1978) Ann. Mat. Pura Appl. , vol.118 , pp. 229-294
    • Furi, M.1    Martelli, M.2    Vignoli, A.3
  • 3
    • 0000869836 scopus 로고
    • A nonlinear spectral approach to surjectivity in Banach spaces
    • FURI, M. and VIGNOLI, A., A nonlinear spectral approach to surjectivity in Banach spaces. J. Funct. Anal., 1975, 20, 304-318.
    • (1975) J. Funct. Anal. , vol.20 , pp. 304-318
    • Furi, M.1    Vignoli, A.2
  • 4
    • 0038944378 scopus 로고
    • Spectrum for nonlinear maps and bifurcation in the nondifferentiable case
    • FURI, M. and VIGNOLI, A., Spectrum for nonlinear maps and bifurcation in the nondifferentiable case. Ann. Mat. Pura Appl., 1977, 113, 265-285.
    • (1977) Ann. Mat. Pura Appl. , vol.113 , pp. 265-285
    • Furi, M.1    Vignoli, A.2
  • 5
    • 0007260317 scopus 로고
    • On spectral theory for nonlinear operators
    • GEORG, K. and MARTELLI, M., On spectral theory for nonlinear operators. J. Funct. Anal., 1977, 24, 140-147.
    • (1977) J. Funct. Anal. , vol.24 , pp. 140-147
    • Georg, K.1    Martelli, M.2
  • 6
    • 0001031586 scopus 로고
    • Regular points, spectrum and eigenfunctions of nonlinear operators
    • KACHUROVSKIJ, R. I., Regular points, spectrum and eigenfunctions of nonlinear operators (Russian). Dokl. Akad. Nauk SSSR, 1969, 188, 274-277; Engl. transl.: Soviet Math. Dokl., 1969, 10, 1101-1105.
    • (1969) Dokl. Akad. Nauk SSSR , vol.188 , pp. 274-277
    • Kachurovskij, R.I.1
  • 7
    • 0004301257 scopus 로고
    • KACHUROVSKIJ, R. I., Regular points, spectrum and eigenfunctions of nonlinear operators (Russian). Dokl. Akad. Nauk SSSR, 1969, 188, 274-277; Engl. transl.: Soviet Math. Dokl., 1969, 10, 1101-1105.
    • (1969) Soviet Math. Dokl. , vol.10 , pp. 1101-1105
  • 8
    • 0002905958 scopus 로고
    • The spectrum of uniformly Lipschitz mappings
    • MADDOX, I. J. and WICKSTEAD, A. W., The spectrum of uniformly Lipschitz mappings. Proc. R. Ir. Acad., 1989, 89A, 101-114.
    • (1989) Proc. R. Ir. Acad. , vol.89 A , pp. 101-114
    • Maddox, I.J.1    Wickstead, A.W.2
  • 10
    • 0042025100 scopus 로고
    • Coincidence degree and solvability of some nonlinear functional equations in normed spaces: A spectral approach
    • MININNI, M., Coincidence degree and solvability of some nonlinear functional equations in normed spaces: a spectral approach. Nonlinear Analysis, 1976, 1, 105-122.
    • (1976) Nonlinear Analysis , vol.1 , pp. 105-122
    • Mininni, M.1
  • 11
    • 84972541095 scopus 로고
    • Existence of a spectrum for nonlinear transformations
    • NEUBERGER, J. W., Existence of a spectrum for nonlinear transformations. Pacific J. Math., 1969, 31, 157-159.
    • (1969) Pacific J. Math. , vol.31 , pp. 157-159
    • Neuberger, J.W.1
  • 12
    • 0009931013 scopus 로고
    • On differentiability and surjectivity of α-Lipschitz mappings
    • PEJSACHOWICZ, J. and VIGNOLI, A., On differentiability and surjectivity of α-Lipschitz mappings. Ann. Mat. Pura Appl., 1974, 101, 49-63.
    • (1974) Ann. Mat. Pura Appl. , vol.101 , pp. 49-63
    • Pejsachowicz, J.1    Vignoli, A.2
  • 13
    • 84985386977 scopus 로고
    • φ-asymptotisches spektrum und surjektivitätssätze vom fredholm-typ für nichtlineare operatoren mit anwendungen
    • WEBER, H., φ-asymptotisches Spektrum und Surjektivitätssätze vom Fredholm-Typ für nichtlineare Operatoren mit Anwendungen. Math. Nachr., 1984, 117, 7-35.
    • (1984) Math. Nachr. , vol.117 , pp. 7-35
    • Weber, H.1
  • 14
    • 0000162636 scopus 로고
    • Sur les espaces completes
    • KURATOWSKI, K., Sur les espaces completes. Fund. Math., 1930, 15, 301-309.
    • (1930) Fund. Math. , vol.15 , pp. 301-309
    • Kuratowski, K.1
  • 15
    • 0002965087 scopus 로고
    • Punti uniti in trasformazioni a codominio non compatto
    • DARBO, G., Punti uniti in trasformazioni a codominio non compatto. Rend. Sem. Mat. Univ. Padova, 1955, 24, 84-92.
    • (1955) Rend. Sem. Mat. Univ. Padova , vol.24 , pp. 84-92
    • Darbo, G.1
  • 16
    • 0001898552 scopus 로고
    • Limit-compact and condensing operators
    • SADOVSKIJ, B. N., Limit-compact and condensing operators (Russian). Uspekhi Mat. Nauk, 1972, 27(1), 81-146; Engl. transl.: Russian Math. Surveys, 1972, 27(1), 85-155.
    • (1972) Uspekhi Mat. Nauk , vol.27 , Issue.1 , pp. 81-146
    • Sadovskij, B.N.1
  • 17
    • 0011115602 scopus 로고
    • SADOVSKIJ, B. N., Limit-compact and condensing operators (Russian). Uspekhi Mat. Nauk, 1972, 27(1), 81-146; Engl. transl.: Russian Math. Surveys, 1972, 27(1), 85-155.
    • (1972) Russian Math. Surveys , vol.27 , Issue.1 , pp. 85-155
  • 19
    • 0011401328 scopus 로고
    • Investigation of some properties of bounded linear operators and of the connection with their q-norm
    • GOL'DENSHTEJN, L. S., GOKHBERG, I. and MARKUS, A. S., Investigation of some properties of bounded linear operators and of the connection with their q-norm (Russian). Uchen. Zapiski Kishin. Gos. Univ., 1957, 29, 29-36.
    • (1957) Uchen. Zapiski Kishin. Gos. Univ. , vol.29 , pp. 29-36
    • Gol'denshtejn, L.S.1    Gokhberg, I.2    Markus, A.S.3
  • 20
    • 0007318663 scopus 로고
    • On a class of nonlinear mappings in Banach spaces
    • GRANAS, A., On a class of nonlinear mappings in Banach spaces. Bull. Acad. Pol. Sci., 1957, 5, 867-870.
    • (1957) Bull. Acad. Pol. Sci. , vol.5 , pp. 867-870
    • Granas, A.1
  • 21
    • 0007185089 scopus 로고
    • On α-contractions and surjectivity
    • VIGNOLI, A., On α-contractions and surjectivity. Boll. Unione Mat. Ital., 1971, 4, 446-455.
    • (1971) Boll. Unione Mat. Ital. , vol.4 , pp. 446-455
    • Vignoli, A.1
  • 23
    • 0000652936 scopus 로고
    • Über mehrdeutige stetige abbildungen
    • BANACH, S. and MAZUR, S., Über mehrdeutige stetige Abbildungen. Studia Math., 1934, 5, 174-178.
    • (1934) Studia Math. , vol.5 , pp. 174-178
    • Banach, S.1    Mazur, S.2
  • 24
    • 0043063613 scopus 로고
    • Proprietè spettrali di certi operatori lineari noncompatti
    • AMBROSETTI, A., Proprietè spettrali di certi operatori lineari noncompatti. Rend. Sem. Mat. Univ. Padova, 1969, 42, 189-200.
    • (1969) Rend. Sem. Mat. Univ. Padova , vol.42 , pp. 189-200
    • Ambrosetti, A.1
  • 25
    • 84972570025 scopus 로고
    • The radius of the essential spectrum
    • NUSSBAUM, R. D., The radius of the essential spectrum. Duke Math. J., 1970, 37, 473-478.
    • (1970) Duke Math. J. , vol.37 , pp. 473-478
    • Nussbaum, R.D.1
  • 29
    • 11744308371 scopus 로고
    • VEB Dt. Verlag Wiss., Berlin
    • TRIEBEL, H., Höhere Analysis. VEB Dt. Verlag Wiss., Berlin, 1972.
    • (1972) Höhere Analysis
    • Triebel, H.1
  • 31
    • 0004537890 scopus 로고
    • Implicit functions, nonlinear integral equations, and the measure of noncompactness of the superposition operator
    • APPELL, J., Implicit functions, nonlinear integral equations, and the measure of noncompactness of the superposition operator. J. Math. Anal Appl., 1981, 83(1), 251-263.
    • (1981) J. Math. Anal Appl. , vol.83 , Issue.1 , pp. 251-263
    • Appell, J.1
  • 32
    • 84979309618 scopus 로고
    • Zur theorie und anwendung des iterationsverfahrens
    • WEISSINGER, J., Zur Theorie und Anwendung des Iterationsverfahrens. Math. Nachr., 1952, 8, 193-212.
    • (1952) Math. Nachr. , vol.8 , pp. 193-212
    • Weissinger, J.1
  • 33
    • 0041560672 scopus 로고
    • Remarks on condensing and k-set-contractive mappings
    • PETRYSHYN, W. V., Remarks on condensing and k-set-contractive mappings. J. Math. Anal. Appl., 1972, 39, 717-741.
    • (1972) J. Math. Anal. Appl. , vol.39 , pp. 717-741
    • Petryshyn, W.V.1
  • 34
    • 21344453471 scopus 로고    scopus 로고
    • A numerical range for nonlinear operators
    • DÖRFNER, M., A numerical range for nonlinear operators. Zeitschr. Anal. Anw., 1996, 15(2), 445-456.
    • (1996) Zeitschr. Anal. Anw. , vol.15 , Issue.2 , pp. 445-456
    • Dörfner, M.1
  • 35
    • 0007191636 scopus 로고
    • Remarks on nonlinear spectral theory
    • EDMUNDS, D. E. and WEBB, J. R. L., Remarks on nonlinear spectral theory. Boll. Unione Mat. Ital., 1983, 2B, 377-390.
    • (1983) Boll. Unione Mat. Ital. , vol.2 B , pp. 377-390
    • Edmunds, D.E.1    Webb, J.R.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.