| Title:
|
Contractive mappings and periodically perturbed conservative systems (English) |
| Author:
|
Mawhin, Jean |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
12 |
| Issue:
|
2 |
| Year:
|
1976 |
| Pages:
|
67-73 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C25 |
| MSC:
|
47J05 |
| idZBL:
|
Zbl 0353.47034 |
| idMR:
|
MR0437858 |
| . |
| Date available:
|
2008-06-06T06:01:54Z |
| Last updated:
|
2012-05-09 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106930 |
| . |
| Reference:
|
[1] Sh. Ahmad: An existence theorem for periodically perturbed conservative systems.Michigan Math. J. 20 (1973) 385-392. Zbl 0294.34029, MR 0346246 |
| Reference:
|
[2] S. Banach: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales.Fundam. Math. 3 (1922) 133-181. |
| Reference:
|
[3] L. Cesari: Alternative methods in nonlinear analysis.Proc. Int. Conf. Differential Equations, Los Angeles, Sept. 74, Academic Press, 1975, 95-148. Zbl 0316.47039, MR 0430884 |
| Reference:
|
[4] C. L. Dolph: Non-linear integral equations of the Hammerstein type.Trans. Amer. Math. Soc. 66 (1949) 289-307. MR 0032923 |
| Reference:
|
[5] H. Ehrmann : On implicit function theorems and the existence of solutions of non-linear equations.L'Enseignement Math. 9 (1963) 129-176. Zbl 0127.08004, MR 0156175 |
| Reference:
|
[6] H. Ehrmann, H. E. Lahmann: Anwendungen des Schauderschen Fixpunktsatzes auf gewisse nichtlineare Integralgleichungen.L'Enseignement Math. 11 (1965) 267-280. Zbl 0196.13002, MR 0202013 |
| Reference:
|
[7] M. Golomb: Zur Theorie der nichtlinearen Integralgleichungen, Integralgleichungssysteme und allgemeinen Funktionalgleichungen.Math. Z. 39 (1935) 45-75. MR 1545488 |
| Reference:
|
[8] J. K. Hale: Applications of alternative problems.Brown Univ. Lecture Notes 71-1, Providence, RI, 1971. |
| Reference:
|
[9] A. Hammerstein: Nichtlineare Integralgleichungen nebst Anwendungen.Acta Math. 54 (1930) 117-176. MR 1555304 |
| Reference:
|
[10] R. Kannan: Periodically perturbed conservative systems.J. Differential Equations, 16 (1974) 506-514. Zbl 0349.34029, MR 0417493 |
| Reference:
|
[11] T. Kato: Perturbation theory for linear operators.Springer, Berlin, 1966. Zbl 0148.12601 |
| Reference:
|
[12] I. Kolodner: Equations of Hammerstein type in Hilbert spaces.J. Math. Mech. 13 (1964) 701-750. Zbl 0149.36401, MR 0171184 |
| Reference:
|
[13] A. C. Lazer, D. A. Sanchez: On periodically perturbed conservative systems.Michigan Math. J. 16 (1969) 193-200. Zbl 0187.34501, MR 0245906 |
| Reference:
|
[14] A. C. Lazer: Application of a lemma on bilinear forms to a problem in nonlinear oscillations.Proc. Amer. Math. Soc. 33 (1972) 89-94. Zbl 0257.34041, MR 0293179 |
| Reference:
|
[15] D. E. Leach: On Poincaré's perturbation theorem and a theorem of W. S. Loud.J. Differential Equations 7 (1970) 34-53. Zbl 0186.15501, MR 0251308 |
| Reference:
|
[16] W. S. Loud: Periodic solutions of nonlinear differential equations of Duffing type.Proc. U.S.-Japan Semin. on Diff. and Funct. Equations, Benjamin, New York, 1967, 199-224. Zbl 0162.12302, MR 0223656 |
| Reference:
|
[17] N. Rouche, J. Mawhin: Equations différentielles ordinaires.vol. 1, Masson, Paris, 1973. Zbl 0289.34001, MR 0481182 |
| Reference:
|
[18] M. M. Vainberg: Variational method and method of monotone operators in the theory of nonlinear equations.Wiley, New York, 1973. Zbl 0279.47022, MR 0467428 |
| . |
