2013•Moscow University Mathematics BulletinRequires access

Spectral properties of a Sturm-Liouville type differential operator with a retarding argument

S. I. Mitrokhin

Abstract

Spectral properties of a differential operator of Sturm-Liouville type are studied in the case of retarding argument with different boundary conditions. The asymptotics of solutions to the corresponding differential equation is studied in the case of a summable potential. An asymptotics of eigenvalues and an asymptotics of eigenfunctions of the differential operator are calculated for each considered case.

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Key concepts: Sturm–Liouville theory, Mathematics, Eigenfunction, Spectral theory of ordinary differential equations, Eigenvalues and eigenvectors, Type (biology), Mathematical analysis, Differential operator