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

被引：9

作者：

Buslaev, AP

Kondrat'ev, VA

Nazarov, AI

机构：

[1] Moscow Inst Automobiles & Roads, Moscow, Russia

[2] Moscow MV Lomonosov State Univ, Moscow 117234, Russia

[3] St Petersburg State Univ, St Petersburg 199034, Russia

来源：

MATHEMATICAL NOTES | 1998年 / 64卷 / 5-6期

关键词：

extremum problem; stability of a column; nonlinear boundary value problem; local asymptotic optimality of nonparametric tests; bifurcation equation;

D O I：

10.1007/BF02313029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The following extremum problem is studied: integral(0)(1) (y "(t))(p) dt / integral(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 integral(R) (max(0, 1 + mu x - /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.

引用

页码：719 / 725

页数：7

共 10 条

[1]

Alekseev VM., 1979, Optimal Control

[2]

[Anonymous], [No title captured], DOI DOI 10.1007/BF00252909

[3] A GENERALIZATION OF WIRTINGER INEQUALITY [J].

DACOROGNA, B ;

GANGBO, W ;

SUBIA, N .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1992, 9 (01) :29-50

[4]

Egorov Yu. V., 1984, USP MAT NAUK, V39, P151

[5]

EGOROV YV, 1990, VESTN MOSK U MAT M+, P75

[6]

EGOROV YV, 1993, CR ACAD SCI I-MATH, V317, P903

[7]

EGOROV YV, 1991, VESTN MOSK U MAT M+, P5

[8]

Lyapunov A. M., 1956, COLLECTED WORKS, V2

[9]

NIKITIN YY, 1995, SSYMPTPTIC EFFECTIVE

[10]

Nirenberg L., 1974, LECT NOTES

← 1 →