SOLVABILITY CONDITIONS FOR ELLIPTIC PROBLEMS WITH NON-FREDHOLM OPERATORS

By Vitaly Volpert, B. Kazmierczak, M. Massot, Z. Peradzyński. 2002

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The paper is devoted to solvability conditions for linear elliptic problems with non-Fredholm operators. We show that the opera- tor becomes normally solvable with a nite-dimensional kernel on properly chosen subspaces. In the particular case of a scalar equation we obtain neces- sary and sucien t 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 perturba- tions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

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