On -differentiable Fredholm operators of nonstationary initial-boundary value problems
Vladimír Ďurikovič; Monika Ďurikovičová
Archivum Mathematicum (2002)
- Volume: 038, Issue: 3, page 227-241
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topĎurikovič, Vladimír, and Ďurikovičová, Monika. "On $F$-differentiable Fredholm operators of nonstationary initial-boundary value problems." Archivum Mathematicum 038.3 (2002): 227-241. <http://eudml.org/doc/248935>.
@article{Ďurikovič2002,
abstract = {We are dealing with Dirichlet, Neumann and Newton type initial-boundary value problems for a general second order nonlinear evolution equation. Using the Fredholm operator theory we establish some sufficient conditions for Fréchet differentiability of associated operators to the given problems. With help of these results the generic properties, existence and continuous dependency of solutions for initial-boundary value problems are studied.},
author = {Ďurikovič, Vladimír, Ďurikovičová, Monika},
journal = {Archivum Mathematicum},
keywords = {Hölder spaces; Fréchet differentiable Fredholm operator of the zero index; critical and singular points of the mixed problem; Hölder spaces; Fréchet differentiable Fredholm operator of the zero index; critical and singular points of the mixed problem},
language = {eng},
number = {3},
pages = {227-241},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On $F$-differentiable Fredholm operators of nonstationary initial-boundary value problems},
url = {http://eudml.org/doc/248935},
volume = {038},
year = {2002},
}
TY - JOUR
AU - Ďurikovič, Vladimír
AU - Ďurikovičová, Monika
TI - On $F$-differentiable Fredholm operators of nonstationary initial-boundary value problems
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 3
SP - 227
EP - 241
AB - We are dealing with Dirichlet, Neumann and Newton type initial-boundary value problems for a general second order nonlinear evolution equation. Using the Fredholm operator theory we establish some sufficient conditions for Fréchet differentiability of associated operators to the given problems. With help of these results the generic properties, existence and continuous dependency of solutions for initial-boundary value problems are studied.
LA - eng
KW - Hölder spaces; Fréchet differentiable Fredholm operator of the zero index; critical and singular points of the mixed problem; Hölder spaces; Fréchet differentiable Fredholm operator of the zero index; critical and singular points of the mixed problem
UR - http://eudml.org/doc/248935
ER -
References
top- Global existence for semilinear parabolic systems, J. Reine Angew. Math. 360 (1985), 47–83. (1985) Zbl0564.35060MR0799657
- Global inversion theorems and applications to nonlinear problems, Conferenze del Seminario di Mathematica dell’ Universitá di Bari, Atti del Seminario di Analisi Funzionale ed Applicazioni, A Survey on the Theoretical and Numerical Trends in Nonlinear Analysis, Gius. Laterza et Figli, Bari, 1976, pp. 211–232. (1976) MR0585116
- Finiteness of the set of solutions of some boundary value problems for ordinary differential equations, Arch. Math. (Brno) 24 (1988), 163–172. (1988) MR0983234
- An initial-boundary value problem for quasi-linear parabolic systems of higher order, Ann. Polon. Math. XXX (1974), 145–164. (1974) MR0350206
- A nonlinear elliptic boundary value problem generated by a parabolic problem, Acta Math. Univ. Comenian. XLIV-XLV (1984), 225–235. (1984) MR0775025
- Some generic properties of nonlinear second order diffusional type problem, Arch. Math. (Brno) 35 (1999), 229–244. (1999) MR1725840
- The investigation of the Green’s matrix for a nonhomogeneous boundary value problems of parabolic type, Trudy Mosk. Mat. Obshch. 23 (1970), 179–234. (in Russian) (1970) MR0367455
- Partial Differential Equations of Parabolic Type, Izd. Mir, Moscow, 1968. (in Russian) (1968)
- Nonlinear Evolution Equations - Global Behaviour of Solutions, Springer - Verlag, Berlin, Heidelberg, New York, 1981. (1981) MR0610796
- Green Matrices of Parabolic Boundary Value Problems, Vyšša Škola, Kijev, 1990. (in Russian) (1990)
- Linejnyje i kvazilinejnyje urovnenija paraboliceskogo tipa, Izd. Nauka, Moscow, 1967. (in Russian) (1967)
- Generic properties of nonlinear boundary value problems, Differential Equations and Mathematical Physics (1992), Academic Press Inc., New York, 217–234. (1992) Zbl0756.47047MR1126697
- Transversal approximation on Banach manifolds, Proc. Sympos. Pure Math. (Global Analysis) 15 (1970), 213–223. (1970) Zbl0206.25705MR0264713
- An infinite dimensional version of Sard’s theorem, Amer. J. Math. 87 (1965), 861–866. (1965) Zbl0143.35301MR0185604
- Fredholm mappings and the generalized boundary value problem, Differential Integral Equations 8 No. 1 (1995), 19–40. (1995) MR1296108
- Introduction of Functional Analysis, John Wiley and Sons, Inc., New York, 1958. (1958) MR0098966
- Functional Analysis, Nauka, Moscow, 1980. (in Russian) (1980) Zbl0517.46001MR0598629
- Functional Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1980. (1980) Zbl0435.46002MR0617913
- Funkcionálna analýza. Nelineárne metódy, Univerzita Komenského, Bratislava, 1989. (1989)
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.