| Title:
|
Some generic properties of nonlinear second order diffusional type problem (English) |
| Author:
|
Ďurikovič, Vladimír |
| Author:
|
Ďurikovičová, Mária |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
229-244 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem. (English) |
| Keyword:
|
Fredholm operator |
| Keyword:
|
Hölder space |
| Keyword:
|
bifurcation set |
| Keyword:
|
parabolic type operator |
| Keyword:
|
locally invertible operator |
| MSC:
|
35G10 |
| MSC:
|
35K55 |
| MSC:
|
47A53 |
| MSC:
|
47F05 |
| MSC:
|
47J05 |
| MSC:
|
47J15 |
| MSC:
|
47N20 |
| MSC:
|
58J35 |
| idZBL:
|
Zbl 1046.35016 |
| idMR:
|
MR1725840 |
| . |
| Date available:
|
2008-06-06T22:23:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107698 |
| . |
| Reference:
|
[1] Brüll, L. and Mawhin, J.: Finiteness of the set of solutions of some boundary value problems for ordinary differential equations.Archivum Mathematicum 24 (1988), 163-172. MR 0983234 |
| Reference:
|
[2] Ďurikovič, V.: An initial-boundary value problem for quasi–linear parabolic systems of higher order.Ann. Palon. Math. XXX (1974), 145-164. MR 0350206 |
| Reference:
|
[3] Ďurikovič, V.: A nonlinear elliptic boundary value problem generated by a parabolic problem.Acta Mathematica Universitatis Comenianae XLIV-XLV (1984), 225-235. MR 0775025 |
| Reference:
|
[4] Ivasišen, S. D.: “Green Matrices of Parabolic Boundary Value Problems”.Vyšša Škola, Kijev, 1990. (in Russian) |
| Reference:
|
[5] Mawhin, J.: Generic properties of nonlinear boundary value problems.Differential Equations and Mathematical Physics (1992), Academic Press Inc., New York, 217-234. Zbl 0756.47047, MR 1126697 |
| Reference:
|
[6] Šeda, V.: Fredholm mappings and the generalized boundary value problem.Differential and Integral Equation 8 Nr.1 (1995), 19-40. MR 1296108 |
| Reference:
|
[7] Šilov, G. J.: “Mathematical analysis”.ALFA, vydavatelstvo technickej a ekonomickej literatury, Bratislava, 1974. (in Slovak) |
| Reference:
|
[8] Taylor, A. E.: Introduction of Functional Analysis.John Wiley and Sons, Inc., New York, 1958. MR 0098966 |
| Reference:
|
[9] Trenogin, V. A.: Functional Analysis.Nauka, Moscow, 1980. (in Russian) Zbl 0517.46001, MR 0598629 |
| Reference:
|
[10] Yosida, K.: Functional Analysis.Springer-Verlag, Berlin, Heidelberg, New York, 1980. Zbl 0435.46002, MR 0617913 |
| . |
