Geodesic
A Note on Upper Bounds for the Eigenvalues of y′′ + λpy=0
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 347-351

Voir la notice de l'article provenant de la source Cambridge University Press

The natural modes of a small planar transversal vibration of a fixed string of unit length and tension are determined by the eigenvalues and associated eigenfunctions of the differential equation (1) subject to the boundary condition (2) where the non-negative function p describes the mass distribution of the string. That the distribution of mass on the string influences the modes of vibration, may be reflected by observing that the eigenvalues determined by the system (1–2) may be considered functions of the density p, λn(p), where λ1(p)<λ2(p)<.... 
Gentry, Rodney D. A Note on Upper Bounds for the Eigenvalues of y′′ + λpy=0. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 347-351. doi: 10.4153/CMB-1975-063-9
@article{10_4153_CMB_1975_063_9,
     author = {Gentry, Rodney D.},
     title = {A {Note} on {Upper} {Bounds} for the {Eigenvalues} of y'' + \ensuremath{\lambda}py=0},
     journal = {Canadian mathematical bulletin},
     pages = {347--351},
     year = {1975},
     volume = {18},
     number = {3},
     doi = {10.4153/CMB-1975-063-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-063-9/}
}
TY  - JOUR
AU  - Gentry, Rodney D.
TI  - A Note on Upper Bounds for the Eigenvalues of y′′ + λpy=0
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 347
EP  - 351
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-063-9/
DO  - 10.4153/CMB-1975-063-9
ID  - 10_4153_CMB_1975_063_9
ER  - 
%0 Journal Article
%A Gentry, Rodney D.
%T A Note on Upper Bounds for the Eigenvalues of y′′ + λpy=0
%J Canadian mathematical bulletin
%D 1975
%P 347-351
%V 18
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-063-9/
%R 10.4153/CMB-1975-063-9
%F 10_4153_CMB_1975_063_9

[1] 1. Banks, D. O., Bounds for the eigenvalues of some vibrating systems\ Pacific J. Math. 10 (1960), 439-474. Google Scholar

[2] 2. Banks, D. O. Upper bounds for the eigenvalues of some vibrating systems, Pacific J. Math. 11 (1961), 1183-1203. Google Scholar

[3] 3. Banks, D. O. Bounds for eigenvalues and generalized convexity, Pacific J. Math. 12 (1963), 1031-1052. Google Scholar

[4] 4. Banks, D. O. Lower bounds for the eigenvalues of a vibrating string whose density satisfies a Lipschitz condition, Pacific J. Math. 20 (1967), 393-410. Google Scholar

[5] 5. Barnes, D., Some isoperimetric inequalities for the eigenvalues of vibrating strings, Pacific J. Math. 29 (1969), 43-61. Google Scholar

[6] 6. Beesack, Paul R., A note on an integral inequality, Proc, Amer. Math. Soc. 8 (1957), 875- 879. Google Scholar

[7] 7. Beesack, P. R. and Schwarz, B., On zeros of solutions of second order linear differential equations, Canadian J. Math. 8 (1956), 504-515. Google Scholar

[8] 8. Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 1, Intersciences Publishers Inc., N.Y. (1966). Google Scholar

[9] 9. Gentry, R. and Banks, D. O., Bounds for functions of eigenvalues for vibrating systems, To appear in J. of Mathematical Analysis and Applications. Google Scholar

[10] 10. Hardy, G. H., Littlewood, J. E., and Polya, G.., Inequalities, Cambridge University Press (1964). Google Scholar

[11] 11. Krein, M. G., On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability, Amer. Math. Soc. Translation, Ser. 2, Vol. 1 (1955), 163- 187. Google Scholar

[12] 12. Schwarz, Binjamin, On the Extrema of the Frequencies of Non-homogeneous Strings with Equimeasurable Density, J. Math, and Mech. V. 10, (1961), 401-422. Google Scholar

[13] 13. Tricomi, F. G., Integral Equations, Interscience Publishers, Inc., N.Y., (1967). Google Scholar

Cité par Sources :