The paper is devoted to solvability conditions for linear elliptic problems with non-Fredholm operators. We show that the operator becomes normally solvable with a finite-dimensional kernel on properly chosen subspaces. In the particular case of a scalar equation we obtain necessary and sufficient solvability conditions. These results are used to apply the implicit function theorem for a nonlinear elliptic problem; we demonstrate the persistence of travelling wave solutions to spatially periodic perturbations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-2-7,
author = {V. Volpert and B. Ka\'zmierczak and M. Massot and Z. Peradzy\'nski},
title = {Solvability conditions for elliptic problems with non-Fredholm operators},
journal = {Applicationes Mathematicae},
volume = {29},
year = {2002},
pages = {219-238},
zbl = {1053.35050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-2-7}
}
V. Volpert; B. Kaźmierczak; M. Massot; Z. Peradzyński. Solvability conditions for elliptic problems with non-Fredholm operators. Applicationes Mathematicae, Tome 29 (2002) pp. 219-238. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-2-7/