On the spectrum of some nonlocal elliptic boundary value problems

The author considers a second order elliptic equation in a cylinder $(0,d)\times G\subset\mathbf R^n$ with the following boundary conditions: the trace of the solution for $x_1=0,d$ is equal to a linear combination of traces for $x_1=d_i$ ($i=1,\dots,m$; $0<d_i<d$), with the trace on the lateral surface of the cylinder equal to zero. It is proved that the spectrum of the operator under consideration is discrete and semibounded, and also that the operator itself is Fredholm. The results are applied to the study of the spectrum of a particular differential-difference operator.
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