| Title:
|
Ein „merkwürdiges” Spektrum für nichtlineare Operatoren (German) |
| Title:
|
A "strange" spectrum for nonlinear operators (English) |
| Author:
|
Appell, Jürgen |
| Language:
|
German |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
221-229 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define a spectrum for Lipschitz continuous nonlinear operators in Banach spaces by means of a certain kind of "pseudo-adjoint" and study some of its properties. (English) |
| Keyword:
|
nonlinear operator |
| Keyword:
|
Lipschitz continuity |
| Keyword:
|
pseudo-adjoint operator |
| Keyword:
|
resolvent set |
| Keyword:
|
spectrum |
| Keyword:
|
eigenvalue |
| Keyword:
|
generalized spectral radius |
| MSC:
|
47A10 |
| MSC:
|
47A25 |
| MSC:
|
47C99 |
| MSC:
|
47H09 |
| MSC:
|
47H12 |
| MSC:
|
47H17 |
| MSC:
|
47H99 |
| MSC:
|
47J10 |
| MSC:
|
47J25 |
| idZBL:
|
Zbl 0940.47053 |
| idMR:
|
MR1780693 |
| DOI:
|
10.21136/MB.1999.126246 |
| . |
| Date available:
|
2009-09-24T21:37:22Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126246 |
| . |
| Reference:
|
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| Reference:
|
[2] Appell J., Dörfner M.: Some spectral theory for nonlinear Operators.Nonlin. Anal. 28 (12) (1997), 1955-1976. Zbl 0876.47042, MR 1436365, 10.1016/S0362-546X(96)00040-5 |
| Reference:
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| Reference:
|
[4] Caselles V.: Duality and nonlinear equations governed by accretive Operators.Publ. Math. Fac. Sci. Besancon 12 (1990), 7-25. Zbl 0766.47029, MR 1034994 |
| Reference:
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[5] Edmunds D.E., Webb J. R. L.: Remarks on nonlinear spectral theory.Boll. Un. Mat. Ital. B 2 (1983), 377-390. MR 0698500 |
| Reference:
|
[6] Feng W.: A new spectral theory for nonlinear Operators and its applications.Abstr. Appl. Anal. 2 (1997), 163-183. Zbl 0952.47047, MR 1604177, 10.1155/S1085337597000328 |
| Reference:
|
[7] Furi M., Martelli M., Vignoli A.: Contributions to the spectral theory for nonlinear Operators in Banach Spaces.Ann. Mat. Pura Appl. 118 (1978), 229-294. Zbl 0409.47043, MR 0533609 |
| Reference:
|
[8] Kachurovskij R. I.: Regular points, spectrum and eigenfunctions of nonlinear operators.Dokl. Akad. Nauk 188 (1969), 274-277. (Russian, Engl, transl.: Soviet Math. Dokl. 10 (1969), 1101-1105.) Zbl 0197.40402, MR 0251599 |
| Reference:
|
[9] Maddox I. J., Wickstead A. W.: The spectrum of uniformly Lipschitz mappings.Proc. Roy. Irish Acad. A 89 (1989), 101-114. Zbl 0661.47048, MR 1021228 |
| Reference:
|
[10] Nashed M. Z.: Differentiability and related properties of nonlinear operators: some aspects of the role of differentials in nonlinear functional analysis.Nonlinear Functional Analysis and Applications (L. B. Rail, ed.). Academic Press, New York, 1971. MR 0276840 |
| Reference:
|
[11] Neuberger J. W.: Existence of a spectrum for nonlinear transformations.Pacific J. Math. 31 (1969), 157-159. Zbl 0182.47203, MR 0259696, 10.2140/pjm.1969.31.157 |
| Reference:
|
[12] Rhodius A.: Der numerische Wertebereich und die Lösbarkeit linearer und nichtlinearer Gleichungen.Math. Nachr. 79 (1977), 343-360. MR 0637086, 10.1002/mana.19770790137 |
| Reference:
|
[13] Shutjaev V. P.: On calculation of a functional in a nonlinear problem using an adjoint equation.Zh. Vychisl. Mat. Mat. Fiz, 31 (1991), 1278-1288. (Russian, Engl. transl.: J. Comput. Math. Math. Phys. 31 (1991), 8-16.) MR 1145198 |
| Reference:
|
[14] Trenogin V. A.: Operators which are adjoint to nonlinear operators in weakly metric spaces.Trudy Mezhd. Konf. 175-let. P. L. Chebysheva, Izdat. MGU 1 (1996), 335-337, (Russian.) |
| Reference:
|
[15] Trenogin V. A.: Properties of resolvent sets and estimates for the resolvent of nonlinear operators.Dokl. Akad. Nauk 359 (1998), 24-26. (Russian.) MR 1668399 |
| Reference:
|
[16] Yamamuro S.: The adjoints of differentiable mappings.J. Austral. Math. Soc. 8 (1968), 397-409. Zbl 0184.17802, MR 0233202, 10.1017/S1446788700006091 |
| . |
