Pacific Journal of Mathematics

Lower bounds for the eigenvalues of a vibrating string whose density satisfies a Lipschitz condition.

Dallas O. Banks

Article information

Source
Pacific J. Math., Volume 20, Number 3 (1967), 393-410.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102992691

Mathematical Reviews number (MathSciNet)
MR0208058

Zentralblatt MATH identifier
0158.21903

Subjects
Primary: 34.30

Citation

Banks, Dallas O. Lower bounds for the eigenvalues of a vibrating string whose density satisfies a Lipschitz condition. Pacific J. Math. 20 (1967), no. 3, 393--410. https://projecteuclid.org/euclid.pjm/1102992691


Export citation

References

  • [mL + (n] , and a/n by [xx + (n - 2)a]/(n -- 1). We now repeat this process, first fixing this new string at its first nodal point
  • [1] D. Banks, Bounds for the eigenvalues of some vibrating systems, Pacific J. Math. 1O (1960), 439-474.
  • [2] D. Banks, Bounds for eigenvalues and generalized convexity,Pacific J. Math. 13 (1963), 1031-1052.
  • [3] R. Courant and D. Hubert, Methods of Mathematical Physics, Vol. 1,Interscience, 1953.
  • [4] M. Krein, On certain problems on the maximumand minimumofcharacteristic values and on Liapunov zones of stability, Amer. Math. Soc. Trans. (2) 1 (1955), 163-187.
  • [5] Z. Nehari, Oscillation criteria for second order linear differentialequations, Trans. Amer. Math. Soc. 85 (1957), 428-445.
  • [6] B. Schwarz, On the extrema of the frequenciesof nonhomogeneous stringswith equimeasurable densities, J. of Math, and Mech. 10 (1961), 401-422.
  • [7] A. Smirnov, Tables of Airy Functions, Pergamon Press, 1960.