This article is cited in 2 papers

Spectral properties of boundary-value problem with a shift for wave equation

N. A. Yessirkegenov^ab, M. A. Sadybekov<sup>b

a</sup> Chair of Fundamental Mathematics, Al-Farabi Kazakh National University, 71 Al-Farabi ave., Almaty, 050040 Republic of Kazakhstan
^b Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010 Republic of Kazakhstan

Abstract: We consider the differential operator given by the wave equation with potential in characteristic triangle and boundary conditions: with shift on the characteristics and oblique derivative on noncharacteristic boundary. We obtain condition for the Volterra property of problem. In remaining cases we show the completeness of the root functions. For cases when the potential depends on a single variable, we study questions of the basis (not basis) property for the system of root functions.

Keywords: wave equation, Riesz basis, regular boundary conditions, eigenvalues, root functions.

UDC: 517.956

Received: 30.07.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:3, 41–46

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