Solvability conditions for some non-Fredholm operators

By V. Vougalter, Vitaly Volpert. Proceedings of the Edinburgh Mathematical Society, 2009

85 citations recorded by the source corpus.

Abstract 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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c94fa4054fd69ea3652c960a8ffe4e704f8e08e2

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In Computational Theory and Mathematics

1. V. Vougalter
2. Vitaly Volpert
3. C. Camere
4. E. Witten
5. Weiping Zhang
6. Nicolas Ginoux
7. I. Shovkovy
8. V. A. Miransky

In Mathematical Physics

1. Vitaly Volpert
2. V. Vougalter
3. E. Witten
4. Nicolas Ginoux
5. C. Camere
6. Weiping Zhang
7. I. Shovkovy
8. V. A. Miransky

Citations in the corpus

• Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems (2012, methodology): “…potential in the original problem when d = 3, such that H a := −∆ x + V (x) − ∆ y − a (1.13) considered on L 2 (D), with D = R 3 × Ω, the Dirichlet Laplacian −∆ y is on L 2 (Ω) as before, the parameter a ≥ 0 and the assumption below is analogous to the one used in [13], [14], [15], [16] and [17].”