# On $F$-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

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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 -

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