Green-Liouville approximation and correct solvability in Lp(ℝ) of the general Sturm-Liouville equation

Nina Chernyavskaya; Leonid Shuster

doi:10.21136/CMJ.2024.0175-23

Green-Liouville approximation and correct solvability in L_p(ℝ) of the general Sturm-Liouville equation

Nina Chernyavskaya, Leonid Shuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider the equation (Formula presented.) where f ∈ L_p(ℝ), p ∈ (1, ∞) and (Formula presented.) For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions r and q under which the above equation is correctly solvable in the space L_p(ℝ), p ∈ (1, ∞).

Original language	English
Pages (from-to)	247-272
Number of pages	26
Journal	Czechoslovak Mathematical Journal
Volume	74
Issue number	1
DOIs	https://doi.org/10.21136/CMJ.2024.0175-23
State	Published - 1 Apr 2024

Keywords

34B24
34B27
Green-Liouville approximation
correct solvability
general Sturm-Liouville equation

ASJC Scopus subject areas

General Mathematics

Access to Document

10.21136/CMJ.2024.0175-23

Cite this

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title = "Green-Liouville approximation and correct solvability in Lp(ℝ) of the general Sturm-Liouville equation",

abstract = "We consider the equation (Formula presented.) where f ∈ Lp(ℝ), p ∈ (1, ∞) and (Formula presented.) For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions r and q under which the above equation is correctly solvable in the space Lp(ℝ), p ∈ (1, ∞).",

keywords = "34B24, 34B27, Green-Liouville approximation, correct solvability, general Sturm-Liouville equation",

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N2 - We consider the equation (Formula presented.) where f ∈ Lp(ℝ), p ∈ (1, ∞) and (Formula presented.) For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions r and q under which the above equation is correctly solvable in the space Lp(ℝ), p ∈ (1, ∞).

AB - We consider the equation (Formula presented.) where f ∈ Lp(ℝ), p ∈ (1, ∞) and (Formula presented.) For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions r and q under which the above equation is correctly solvable in the space Lp(ℝ), p ∈ (1, ∞).

KW - 34B24

KW - 34B27

KW - Green-Liouville approximation

KW - correct solvability

KW - general Sturm-Liouville equation

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