Solvability conditions for elliptic problems with non-Fredholm operators
Volume 29 / 2002
Applicationes Mathematicae 29 (2002), 219-238
MSC: Primary 35J45; Secondary 47A53, 47F05.
DOI: 10.4064/am29-2-7
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.
