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non-fredholm operators

Proceedings of the Edinburgh Mathematical Society (1)

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Solvability conditions for some non-Fredholm operators
Part of
- Spectral theory and eigenvalue problems
- Elliptic equations and systems
Vitali Vougalter, Vitaly Volpert
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 1 / February 2011

Published online by Cambridge University Press:

30 November 2010, pp. 249-271
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We obtain solvability conditions for some elliptic equations involving non-Fredholm operators with the methods of spectral theory and scattering theory for Schrödinger-type operators. One of the main results of the paper concerns solvability conditions for the equation –Δu + V(x)u–au = f where a ≥ 0. The conditions are formulated in terms of orthogonality of the function f to the solutions of the homogeneous adjoint equation.