Sunto
Si introduce una definizione di spettro σ(f) per applicazioni continue definite in uno spazio di Banach. Tale definizione coincide con quella classica nel caso in cui f sia lineare e continua. Alcuni dei risultati più noti della teoria spettrale lineare vengono estesi al caso non lineare. In particolare si dimostra che σ(f) è chiuso e che la sua frontiera è contenuta nello spettro puntuale approssimato σπ(f).
Article PDF
References
S. K. Berberian,Lectures in Functional Analysis and Operalor Theory, Springer-Verlag, 1974.
J. Canavati,A theory of numerical range for nonlinear operators, to appear.
G. Darbo,Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Padova,24 (1955), pp. 84–92.
J. Dugundji,An extension of Tietze's theorem, Pacific J. Math.,1 (1951), pp. 353–367.
N. Dunford - J. T. Schwartz,Linear Operators, Interscience Publishers, 1958.
S. Fučik - J. Nečas - J. Souček - V. Souček,Spectral Analysis of Nonlinear Operators, Lectures Notes in Mathematics, no. 346, Springer-Verlag, 1973.
M. Furi -M. Martelli,On α-Lipschitz retractions of the unit closed ball onto its boundary, Accad. Naz. Lincei,57 (1974), pp. 61–65.
M. Furi -A. Vignoli,On a property of the unit sphere in a linear normed space, Bull. Acad. Pol. Sci.,18 (1970), pp. 333–334.
M. Furi -A. Vignoli,A nonlinear spectral approach to surjectivity in Banach spaces, J. Funct. Anal.,20 (1975), pp. 304–318.
M. Furi -A. Vignoli,Spectrum for nonlinear maps and bifurcation in the non differentiable case, Ann. Mat. Pura Appl.,113 (1977), pp. 265–285.
M. Furi -M. Martelli -A. Vignoli,Stably solvable operators in Banach spaces, Accad. Naz. Lincei,60 (1976), pp. 21–26.
K. Georg -M. Martelli,On spectral theory for nonlinear opertors, J. Funct. Anal.,24 (1977), pp. 111–119.
A. Granas,The theory of compact vector fields and some applications to the topology of functional spaces, Rozprawy Matematyezne, Warszawa,30 (1962).
S. T. Hu,Homotopy theory, Academic Press, 1959.
T. Kato,Perturbation theory for linear operators, Springer-Verlag, 1966.
M. A. Krasnosel'skij,Topological methods in the theory of nonlinear integral equations, Pergamon Press, 1964.
C. Kuratowski,Sur les espaces complètes, Fund. Math.,15 (1930), pp. 301–335.
E. Michael,Continuous selections I, Ann. of Math.,63 (1956), pp. 361–382.
L. Nirenberg,An application of generalized degree to a class of nonlinear problems, Colloq. d'Analyse Math., Liège (1971), pp. 57–74.
R. D. Nussbaum,Some fixed point theorems, Bull. Amer. Math. Soc.,77 (1971), pp. 360–365.
R. D. Nussbaum,The fixed point index for local condensing maps, Ann. Mat. Pura Appl.,89 (1971), pp. 217–258.
B. N. Sadovskij,A fixed point principle, Funk. Anal. Prilož.,1 (1967), pp. 74–79.
J. Schauder,Über lineare elliptische Differentialgleichunger zweiter Ordnung, Math. Z.,38 (1934), pp. 257–282.
A. E. Taylor,Introduction to Functional Analysis, John Wiley & Sons Inc., 1958.
G. Hetzer,Some remarks on φ +-operators and on the coincidence degree for a Fredholm equation with noncompact nonlinear perturbation, Ann. Soc. Sci. Bruxelles, Ser. I,89 (1975), pp. 497–508.
Author information
Authors and Affiliations
Additional information
Entrata in Redazione il 17 giugno 1977.
Work performed under the auspices of the National Research Council of Italy (C.N.R.).
Rights and permissions
About this article
Cite this article
Furi, M., Martelli, M. & Vignoli, A. Contributions to the spectral theory for nonlinear operators in Banach spaces. Annali di Matematica 118, 229–294 (1978). https://doi.org/10.1007/BF02415132
Issue Date:
DOI: https://doi.org/10.1007/BF02415132