Pacific Journal of Mathematics

Inequalities for eigenvalues of the biharmonic operator.

G. N. Hile and R. Z. Yeh

Article information

Source
Pacific J. Math., Volume 112, Number 1 (1984), 115-133.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102710102

Mathematical Reviews number (MathSciNet)
MR739143

Zentralblatt MATH identifier
0541.35059

Subjects
Primary: 35P15: Estimation of eigenvalues, upper and lower bounds

Citation

Hile, G. N.; Yeh, R. Z. Inequalities for eigenvalues of the biharmonic operator. Pacific J. Math. 112 (1984), no. 1, 115--133. https://projecteuclid.org/euclid.pjm/1102710102


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References

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  • [2] G. Chiti, A boundfor the ratio of thefirst two eigenvalues of a membrane, to appear.
  • [3] H. L. DeVries, On the upperboundfor the ratio of thefirst two membrane eigenvalues, Z. Nauturforsch. A., 22 (1967), 152-153.
  • [4] G. N. Hile and M. H. Protter, Inequalities for eigenvalues of the Laplacian, Indiana Univ. Math. J., 29 (1980), 523-538.
  • [5] P. Marcellini, Bounds for the third membrane eigenvalues, J. Differential Equations, 37 (1980), 438-443.
  • [6] L. E. Payne, G. Polya and H. F. Weinberger, On the ratio of consecutive eigenvalues, J. Math, and Physics, 35 (1956), 289-298.