| Title:
|
Hard implicit function theorem and small periodic solutions to partial differential equations (English) |
| Author:
|
Krejčí, Pavel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
25 |
| Issue:
|
3 |
| Year:
|
1984 |
| Pages:
|
519-536 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35B10 |
| MSC:
|
35G30 |
| MSC:
|
47H15 |
| MSC:
|
47H17 |
| MSC:
|
47J25 |
| MSC:
|
58C15 |
| idZBL:
|
Zbl 0567.35007 |
| idMR:
|
MR775567 |
| . |
| Date available:
|
2008-06-05T21:19:14Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106323 |
| . |
| Reference:
|
[1] M. ALTMAN: A series of papers on nonlinear evolution equations.Nonlin. Anal., Theory, Meth., Appl. 8 (1984), No. 5, pp. 457 - 499. MR 0741601 |
| Reference:
|
[2] W. CRAIG: A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations.Ann. Scuola Norm. Sup. Pisa, ser. IV, vol. X (1983), pp. 125 - 168. Zbl 0518.35057, MR 0713113 |
| Reference:
|
[3] B. D. CRAVEN M. Z. NASHED: Generalized implicit function theorems when the derivative has no bounded inverse.Nonlin. Anal., Theory, Meth., Appl. 6 (1982), pp. 375-387. MR 0654813 |
| Reference:
|
[4] M. R. HESTENES: Extension of the range of a differentiable function.Duke Math. J. 8 (1941), pp. 183 - 192. Zbl 0024.38602, MR 0003434 |
| Reference:
|
[5] L. HÖRMANDER: The boundary problems of physical geodesy.Arch. Rat. Keen. Anal. 62 (1976), pp. 1 - 52. MR 0602181 |
| Reference:
|
[6] S. KLAINERMAN: Global existence for nonlinear wave equations.Comm. Pure Appl. Math. 33 (1980), pp. 43 - 101. Zbl 0405.35056, MR 0544044 |
| Reference:
|
[7] P. KREJČÍ: Periodic vibrations of the electromagnetic field in ferromagnetic media.(in Czech). Candidate thesis, Mathematical Institute of the Czechoslovak Academy of Sciences, Prague, 1984. |
| Reference:
|
[8] J. MOSER: A new technique for the construction of solutions of nonlinear differential equations.Proc. Nat. Acad. Sci. 47 (1961), pp. 1824 - 1831. Zbl 0104.30503, MR 0132859 |
| Reference:
|
[9] J. MOSER: A rapidly-convergent iteration method and nonlinear differential equations.Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265 - 315, 499 - 535. |
| Reference:
|
[10] J. NASH: The embedding problem for Riemannian manifolds.Ann. of Math. 63 (1956), pp. 20 - 63. MR 0075639 |
| Reference:
|
[11] L. NIRENBERG: On elliptic partial differential equations.Ann. Scuola Norm. Sup. Pisa, 13 (1959), pp. 115 - 162. Zbl 0088.07601, MR 0109940 |
| Reference:
|
[12] H. PETZELTOVÁ: Application of Moser's method to a certain type of evolution equations.Czech. Math. J. 33 (1983), pp. 427 - 434. Zbl 0547.35081, MR 0718925 |
| Reference:
|
[13] V. PTÁK: A modification of Newton's method.Čas. Pěst. Mat. 101 (1976), pp. 188 - 194. Zbl 0328.46013, MR 0443326 |
| Reference:
|
[14] P. H. RABINOWITZ: Periodic solutions of nonlinear hyperbolic partial differential equations II.Comm. Pure Appl. Math. 22 (1969), pp. 15 - 39. Zbl 0157.17301, MR 0236504 |
| Reference:
|
[15] J. T. SCHWARTZ: On Nash's implicit functional theorem.Comm. Pure Appl. Math. 13 (1960), pp. 509 - 530. Zbl 0178.51002, MR 0114144 |
| Reference:
|
[16] J. SHATAH: Global existence of small solutions to nonlinear evolution equations.J. Diff. Eq. 46 (1982), pp.409 - 425. Zbl 0518.35046, MR 0681231 |
| Reference:
|
[17] Y. SHIBATA: On the global existence of classical solutions of mixed problem for some second order non-linear hyperbolic operators with dissipative term in the interior domain.Funkc. Ekv. 25 (1982), pp. 303 - 345. MR 0707564 |
| Reference:
|
[18] Y. SHIBATA: On the global existence of classical solutions of second order fully nonlinear hyperbolic equations with first-order dissipation in the exterior domain.Tsukuba J. Math. 7 (1983), pp. 1 - 68. Zbl 0524.35071, MR 0703667 |
| . |
