scholarly journals Solvability conditions for some non-Fredholm operators

2010 ◽  
Vol 54 (1) ◽  
pp. 249-271 ◽  
Author(s):  
Vitali Vougalter ◽  
Vitaly Volpert
Keyword(s):  
Spectral Theory ◽  
Elliptic Equations ◽  
Scattering Theory ◽  
Adjoint Equation ◽  
Fredholm Operators ◽  
Solvability Conditions ◽  
Non Fredholm Operators ◽  
Schrödinger Type Operators

AbstractWe 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=fwhere a ≥ 0. The conditions are formulated in terms of orthogonality of the functionfto the solutions of the homogeneous adjoint equation.

scholarly journals Solvability conditions for elliptic problems with non-Fredholm operators

2002 ◽  
Vol 29 (2) ◽  
pp. 219-238 ◽  
Author(s):  
V. Volpert ◽  
B. Kaźmierczak ◽  
M. Massot ◽  
Z. Peradzyński
Keyword(s):  
Elliptic Problems ◽  
Fredholm Operators ◽  
Solvability Conditions ◽  
Non Fredholm Operators

scholarly journals Dynamics and spectral theory of quasi-periodic Schrödinger-type operators

2016 ◽  
Vol 37 (8) ◽  
pp. 2353-2393 ◽  
Author(s):  
C. A. MARX ◽  
S. JITOMIRSKAYA
Keyword(s):  
Dynamical Systems ◽  
Spectral Theory ◽  
Point Of View ◽  
Schrödinger Type Operators

We survey the theory of quasi-periodic Schrödinger-type operators, focusing on the advances made since the early 2000s by adopting a dynamical systems point of view.

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