Geodesic
Solvability conditions for elliptic problems with non-Fredholm operators
V. Volpert1 ; B. Ka/xmierczak2 ; M. Massot3 ; Z. Peradzy/nski4
1 Laboratoire de Mathématiques Appliquées UMR 5585 CNRS, Université Lyon 1 69622 Villeurbanne, France
2 Institute of Fundamental Technological Research /Swi/etokrzyska 21 00-049 Warszawa, Poland
3 Laboratoire de Mathématiques Appliquées UMR 5585 CNRS Université Lyon 1, 69622 Villeurbanne, France
4 Department of Mathematics, Computer Science and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Applicationes Mathematicae, Tome 29 (2002) no. 2, pp. 219-238 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am29-2-7
Keywords: paper devoted solvability conditions linear elliptic problems non fredholm operators operator becomes normally solvable finite dimensional kernel properly chosen subspaces particular scalar equation obtain necessary sufficient solvability conditions these results apply implicit function theorem nonlinear elliptic problem demonstrate persistence travelling wave solutions spatially periodic perturbations

V. Volpert 1 ; B. Ka/xmierczak 2 ; M. Massot 3 ; Z. Peradzy/nski 4

1 Laboratoire de Mathématiques Appliquées UMR 5585 CNRS, Université Lyon 1 69622 Villeurbanne, France
2 Institute of Fundamental Technological Research /Swi/etokrzyska 21 00-049 Warszawa, Poland
3 Laboratoire de Mathématiques Appliquées UMR 5585 CNRS Université Lyon 1, 69622 Villeurbanne, France
4 Department of Mathematics, Computer Science and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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     author = {V. Volpert and B. Ka/xmierczak and M. Massot and Z. Peradzy/nski},
     title = {Solvability conditions for elliptic problems
 with {non-Fredholm} operators},
     journal = {Applicationes Mathematicae},
     pages = {219--238},
     year = {2002},
     volume = {29},
     number = {2},
     doi = {10.4064/am29-2-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am29-2-7/}
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V. Volpert; B. Ka/xmierczak; M. Massot; Z. Peradzy/nski. Solvability conditions for elliptic problems
 with non-Fredholm operators. Applicationes Mathematicae, Tome 29 (2002) no. 2, pp. 219-238. doi: 10.4064/am29-2-7

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