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2018•Russian MathematicsRequires access

Asymptotics of Eigenvalues of Differential Operator With Alternating Weight Function

Sergei Ivanovich Mitrokhin

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Abstract

We study a differential operator of the sixth order with an alternating weight function. The potential of the operator has a first-order discontinuity at some point of the segment, where the operator is being considered. The boundary conditions are separated. We study the asymptotics of solutions to the corresponding differential equations and the asymptotics of eigenvalues of the considered differential operator.

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What this paper is about

We study a differential operator of the sixth order with an alternating weight function. The potential of the operator has a first-order discontinuity at some point of the segment, where the operator is being considered. The boundary conditions are separated. We study the asymptotics of solutions to the corresponding differential equations and the asymptotics of eigenvalues of the considered differential operator.

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OpenAlex reports 10 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We study a differential operator of the sixth order with an alternating weight function. The potential of the operator has a first-order discontinuity at some point of the segment, where the operator is being considered. The boundary conditions are separated. We study the asymptotics of solutions to the corresponding differential equations and the asymptotics of eigenvalues of the considered differential operator.

Key concepts: Mathematics, Semi-elliptic operator, Differential operator, Mathematical analysis, Eigenvalues and eigenvectors, Operator (biology), Hypoelliptic operator, Symbol of a differential operator

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