Solvability conditions for elliptic problems with non-Fredholm operators

V. Volpert; B. Kaźmierczak; M. Massot; Z. Peradzyński

Applicationes Mathematicae (2002)

  • Volume: 29, Issue: 2, page 219-238
  • ISSN: 1233-7234

Abstract

top
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.

How to cite

top

V. Volpert, et al. "Solvability conditions for elliptic problems with non-Fredholm operators." Applicationes Mathematicae 29.2 (2002): 219-238. <http://eudml.org/doc/279074>.

@article{V2002,
abstract = {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.},
author = {V. Volpert, B. Kaźmierczak, M. Massot, Z. Peradzyński},
journal = {Applicationes Mathematicae},
keywords = {non-Fredholm operators; normal solvability; implicit function theorem},
language = {eng},
number = {2},
pages = {219-238},
title = {Solvability conditions for elliptic problems with non-Fredholm operators},
url = {http://eudml.org/doc/279074},
volume = {29},
year = {2002},
}

TY - JOUR
AU - V. Volpert
AU - B. Kaźmierczak
AU - M. Massot
AU - Z. Peradzyński
TI - Solvability conditions for elliptic problems with non-Fredholm operators
JO - Applicationes Mathematicae
PY - 2002
VL - 29
IS - 2
SP - 219
EP - 238
AB - 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.
LA - eng
KW - non-Fredholm operators; normal solvability; implicit function theorem
UR - http://eudml.org/doc/279074
ER -

NotesEmbed ?

top

You 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.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.