| Title:
|
Periodic solutions of a nonlinear evolution problem (English) |
| Author:
|
de Oliveira Castro, Nelson Nery |
| Author:
|
de Andrade, Nirzi G. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
5 |
| Year:
|
2002 |
| Pages:
|
381-396 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove existence of periodic solutions to a nonlinear evolution system of second order partial differential equations involving the pseudo-Laplacian operator. To show the existence of periodic solutions we use Faedo-Galerkin method with a Schauder fixed point argument. (English) |
| Keyword:
|
periodic solutions |
| Keyword:
|
fixed points |
| Keyword:
|
nonlinear evolution problem |
| Keyword:
|
pseudo-Laplacian |
| MSC:
|
35B10 |
| MSC:
|
35L99 |
| MSC:
|
35Q99 |
| idZBL:
|
Zbl 1090.35548 |
| idMR:
|
MR1924676 |
| DOI:
|
10.1023/A:1021757823679 |
| . |
| Date available:
|
2009-09-22T18:10:52Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134503 |
| . |
| Reference:
|
[1] F. E. Browder, Bui An Ton: Nonlinear functional equations in Banach spaces and elliptic super regularization.Math. Z. 105 (1968), 177–195. MR 0232256, 10.1007/BF01109897 |
| Reference:
|
[2] N. N. Castro: Existence and asymptotic behaviour of solutions of a nonlinear evolution problem.Appl. Math. 42 (1997), 411–420. Zbl 0940.35139, MR 1475050, 10.1023/A:1022251012703 |
| Reference:
|
[3] J. Cronin: Fixed Point and Topological Degree in Nonlinear Analysis. Mathematical Surveys, No. 11.Amer. Math. Soc., Providence, 1964. MR 0164101 |
| Reference:
|
[4] T. Kakita: On the existence of time periodic solutions of some nonlinear evolution equations.Appl. Anal. 4 (1974), 63–76. MR 0454278, 10.1080/00036817408839083 |
| Reference:
|
[5] J. L. Lions: Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires.Dunod, Paris, 1969. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[6] L. A. Medeiros, M. M. Miranda: Weak solutions of nonlinear Klein-Gordon equations.Ann. Math. Pura Appl. IV, ser. 146 (1987), 173–183. MR 0916692 |
| Reference:
|
[7] I. Segal: Nonlinear partial differential equations in quantum field theory.Proc. Sympos. Appl. Math. Amer. Math. Soc. 17 (1965), 210–226. Zbl 0152.23902, MR 0202406, 10.1090/psapm/017/0202406 |
| Reference:
|
[8] M. Tsutsumi: Some nonlinear evolution equations of second order.Proc. Japan. Acad. Ser. A Math. Sci. 47 (1971), 950–955. Zbl 0258.35017, MR 0312023 |
| Reference:
|
[9] K. Yosida: Equations Différentielles et Intégrales.Dunod, Paris, 1971. Zbl 0231.34002, MR 0344557 |
| Reference:
|
[10] E. Zeidler: Nonlinear Functional Analysis and its Applications: I—Fixed-Point Theorems.Springer-Verlag, New York, 1986. Zbl 0583.47050, MR 0816732 |
| . |
