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.
@article{107836,
author = {Vladim\'\i r \v Durikovi\v c and Monika \v Durikovi\v cov\'a},
title = {On $F$-differentiable Fredholm operators of nonstationary initial-boundary value problems},
journal = {Archivum Mathematicum},
volume = {038},
year = {2002},
pages = {227-241},
zbl = {1090.58012},
mrnumber = {1921594},
language = {en},
url = {http://dml.mathdoc.fr/item/107836}
}
Ďurikovič, Vladimír; Ďurikovičová, Monika. On $F$-differentiable Fredholm operators of nonstationary initial-boundary value problems. Archivum Mathematicum, Tome 038 (2002) pp. 227-241. http://gdmltest.u-ga.fr/item/107836/
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