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 -