Fredholm theory and semilinear equations without resonance involving noncompact perturbations. I.
Milojević, P.S. (1987)
Publications de l'Institut Mathématique. Nouvelle Série
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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...