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On discreteness of spectrum of a functional differential operator

Sergey LabovskiyMário Frengue Getimane — 2014

Mathematica Bohemica

We study conditions of discreteness of spectrum of the functional-differential operator u = - u ' ' + p ( x ) u ( x ) + - ( u ( x ) - u ( s ) ) d s r ( x , s ) on ( - , ) . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.

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