Stable perturbations of boundary problems for differential equations

Z. Yu. Fazullin, Baltabek Esmatovich Kanguzhin, А. А. Seitova

2018

Full text Open access: Gold Metadata (CSL-JSON)
DOI 10.31489/2018m4/38-43
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

Stable perturbations of boundary problems for differential equationsIn this paper, we expand the class of nondegenerate two-point boundary value problems for the Sturm-Liouville equation, which have a complete system of eigenfunctions and associated functions in special function spaces.Such spaces depend on the length of support of the potential of the Sturm-Liouville equation.The formulated results clarify well-known results of V.A. Marchenko.Two-point boundary value problems for the Sturm-Liouville equation are divided into degenerate and nondegenerate boundary conditions in the sense of V.A. Marchenko.The main result of V.A. Marchenko asserts that systems of eigenfunctions and associated functions of nondegenerate boundary value problems for the Sturm-Liouville equation form a complete system of functions in the space of square-summable functions.In this paper, the result of V.A. Marchenko is clarified in the following direction.There are operators with a complete system of eigenfunctions and associated functions in the space of square-summable functions among the degenerate boundary value problems in the sense of V.A. Marchenko.The presence of the completeness property depends on the length of support of the measure which is antisymmetry to the potential of the Sturm-Liouville equation.