Solvability conditions for elliptic problems with non-Fredholm operators

Tom 29 / 2002

V. Volpert, B. Ka/xmierczak, M. Massot, Z. Peradzy/nski Applicationes Mathematicae 29 (2002), 219-238 MSC: Primary 35J45; Secondary 47A53, 47F05. DOI: 10.4064/am29-2-7

Streszczenie

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.

Autorzy

  • V. VolpertLaboratoire de Mathématiques Appliquées
    UMR 5585 CNRS, Université Lyon 1
    69622 Villeurbanne, France
    e-mail
  • B. Ka/xmierczakInstitute of Fundamental Technological Research
    /Swi/etokrzyska 21
    00-049 Warszawa, Poland
    e-mail
  • M. MassotLaboratoire de Mathématiques Appliquées
    UMR 5585 CNRS
    Université Lyon 1, 69622 Villeurbanne, France
    e-mail
  • Z. Peradzy/nskiDepartment of Mathematics,
    Computer Science and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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