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On a family of extremum problems and the properties of an integral. / Buslaev, A. P.; Kondrat'ev, V. A.; Nazarov, A. I.

In: Mathematical Notes, Vol. 64, No. 5-6, 01.12.1998, p. 719-725.

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

Harvard

Buslaev, AP, Kondrat'ev, VA & Nazarov, AI 1998, 'On a family of extremum problems and the properties of an integral', Mathematical Notes, vol. 64, no. 5-6, pp. 719-725.

APA

Buslaev, A. P., Kondrat'ev, V. A., & Nazarov, A. I. (1998). On a family of extremum problems and the properties of an integral. Mathematical Notes, 64(5-6), 719-725.

Vancouver

Buslaev AP, Kondrat'ev VA, Nazarov AI. On a family of extremum problems and the properties of an integral. Mathematical Notes. 1998 Dec 1;64(5-6):719-725.

Author

Buslaev, A. P. ; Kondrat'ev, V. A. ; Nazarov, A. I. / On a family of extremum problems and the properties of an integral. In: Mathematical Notes. 1998 ; Vol. 64, No. 5-6. pp. 719-725.

BibTeX

@article{b95051d46c644e9b902d56e31b4d5b90,
title = "On a family of extremum problems and the properties of an integral",
abstract = "The following extremum problem is studied: ∫ 0 1(y ″(t)) p dt / ∫ 0 1(y ′(t)) q dt → min over all y, with y(0) = y(1) = 0 and y′(0) = y′(1) =0, which leads to the integral ∫ℝ(max(0, 1 + μx - |x| q)) 1/p′ dx and yields exact estimates for the eigenvalues of differential operators in the generalized Lagrange problem on the stability of a column.",
keywords = "Bifurcation equation, Extremum problem, Local asymptotic optimality of nonparametric tests, Nonlinear boundary value problem, Stability of a column",
author = "Buslaev, {A. P.} and Kondrat'ev, {V. A.} and Nazarov, {A. I.}",
year = "1998",
month = dec,
day = "1",
language = "English",
volume = "64",
pages = "719--725",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "5-6",

}

RIS

TY - JOUR

T1 - On a family of extremum problems and the properties of an integral

AU - Buslaev, A. P.

AU - Kondrat'ev, V. A.

AU - Nazarov, A. I.

PY - 1998/12/1

Y1 - 1998/12/1

N2 - The following extremum problem is studied: ∫ 0 1(y ″(t)) p dt / ∫ 0 1(y ′(t)) q dt → min over all y, with y(0) = y(1) = 0 and y′(0) = y′(1) =0, which leads to the integral ∫ℝ(max(0, 1 + μx - |x| q)) 1/p′ dx and yields exact estimates for the eigenvalues of differential operators in the generalized Lagrange problem on the stability of a column.

AB - The following extremum problem is studied: ∫ 0 1(y ″(t)) p dt / ∫ 0 1(y ′(t)) q dt → min over all y, with y(0) = y(1) = 0 and y′(0) = y′(1) =0, which leads to the integral ∫ℝ(max(0, 1 + μx - |x| q)) 1/p′ dx and yields exact estimates for the eigenvalues of differential operators in the generalized Lagrange problem on the stability of a column.

KW - Bifurcation equation

KW - Extremum problem

KW - Local asymptotic optimality of nonparametric tests

KW - Nonlinear boundary value problem

KW - Stability of a column

UR - http://www.scopus.com/inward/record.url?scp=0038185009&partnerID=8YFLogxK

M3 - Article

VL - 64

SP - 719

EP - 725

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 5-6

ER -

ID: 45874566