| Title:
|
Discontinuous wave equations and a topological degree for some classes of multi-valued mappings (English) |
| Author:
|
Fečkan, Michal |
| Author:
|
Kollár, Richard |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
15-32 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Leray-Schauder degree is extended to certain multi-valued mappings on separable Hilbert spaces with applications to the existence of weak periodic solutions of discontinuous semilinear wave equations with fixed ends. (English) |
| Keyword:
|
discontinuous wave equations |
| Keyword:
|
topological degree |
| Keyword:
|
multi-valued mappings |
| MSC:
|
35L05 |
| MSC:
|
35L70 |
| MSC:
|
47H17 |
| MSC:
|
58C06 |
| idZBL:
|
Zbl 1060.35524 |
| idMR:
|
MR1666854 |
| DOI:
|
10.1023/A:1022216119044 |
| . |
| Date available:
|
2009-09-22T17:59:45Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134403 |
| . |
| Reference:
|
[1] J. Berkovits: Some bifurcation results for a class of semilinear equations via topological degree method.Bull. Soc. Math. Belg. 44 (1992), 237–247. Zbl 0783.47069, MR 1314039 |
| Reference:
|
[2] J. Berkovits & V. Mustonen: An extension of Leray-Schauder degree and applications to nonlinear wave equations.Diff. Int. Eqns. 3 (1990), 945–963. MR 1059342 |
| Reference:
|
[3] J. Berkovits & V. Mustonen: Topological degree for perturbations of linear maximal monotone mappings and applications to a class of parabolic problems.Rend. Mat. VII-12 (1992), 597–621. MR 1205967 |
| Reference:
|
[4] H. Brezis: Periodic solutions of nonlinear vibrating strings and duality principles.Bull. Amer. Math. Soc. 8 (1983), 409–426. Zbl 0537.35055, MR 0693957, 10.1090/S0273-0979-1983-15105-4 |
| Reference:
|
[5] F. E. Browder: Fixed point theory and nonlinear problems.Bull. Amer. Math. Soc. 9 (1983), 1–39. Zbl 0533.47053, MR 0699315, 10.1090/S0273-0979-1983-15153-4 |
| Reference:
|
[6] K. C. Chang: Free boundary problems and the set-valued mappings.J. Differential Eqns. 49 (1983), 1–28. Zbl 0533.35088, MR 0704263, 10.1016/0022-0396(83)90018-9 |
| Reference:
|
[7] K. Deimling: Nonlinear Functional Analysis.Springer-Verlag, Berlin, 1985. Zbl 0559.47040, MR 0787404 |
| Reference:
|
[8] H. Gajewski, K. Gröger & K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie-Verlag, Berlin, 1974. MR 0636412 |
| Reference:
|
[9] A. Kittilä: On the topological degree for a class of mappings of monotone type and applications to strongly nonlinear elliptic problems.Ann. Acad. Sci. Fenn. Ser. A I Math. Disser. 91 (1994). MR 1263099 |
| Reference:
|
[10] W. Rudin: Real and Complex Analysis.McGraw-Hill, Inc., New York, 1974. Zbl 0278.26001, MR 0344043 |
| . |
