Solvability and spectrum of the third boundary problem for an elliptic differential-difference equation (Q1316883)

We study the solvability and the spectrum of the third boundary problem for a second order elliptic differential-difference equation in a bounded domain. As it turns out the symbol of an elliptic differential-difference equation can be of variable sign while at the same time the spectrum of the problem is semibounded, discrete, and of finite multiplicity.