Solvability conditions for elliptic problems with non-Fredholm operators

• Autorzy: V. Volpert , B. Kaźmierczak , M. Massot , Z. Peradzyński
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 47F05: Partial differential operators (should also be assigned at least one other classification number in section 47)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2002
• Tom: 29
• Numer: 2
• Strony: 219-238

Daty

wydano

2002

Twórcy

autor

V. Volpert

• Laboratoire de Mathématiques Appliquées, UMR 5585 CNRS, Université Lyon 1, 69622 Villeurbanne, France

autor

B. Kaźmierczak

• Institute of Fundamental Technological Research, Świętokrzyska 21, 00-049 Warszawa, Poland

autor

M. Massot

• Laboratoire de Mathématiques Appliquées, UMR 5585 CNRS, Université Lyon 1, 69622 Villeurbanne, France

autor

Z. Peradzyński

• Department of Mathematics, Computer Science and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/am29-2-7