Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

On lower bounds of the natural frequencies of inhomogeneous plates


Author: V. Komkov
Journal: Quart. Appl. Math. 31 (1974), 395-401
MSC: Primary 35J40
DOI: https://doi.org/10.1090/qam/425349
MathSciNet review: 425349
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] N. Aronszajn, The Raleigh-Ritz method and A. Weinstein method for approximation of eigenvalues, I, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 474-480
  • [2] -, II, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 594-601
  • [3] -, Approximation methods for eigenvalues of completely continuous symmetric operators, in Proc. Symp. Spectral Theory and Differential Problems, Oklahoma State Univ., Stillwater, Okla., 1951
  • [4] N. Bazley and D. W. Fox, Truncation in the method of intermediate problems for lower bounds to eigenvalues, J. Res. Nat. Bur. Stds. 65B, (1961) MR 0142897
  • [5] -, Methods for lower bounds to frequencies of continuous elastic systems, John Hopkins Univ. Applied Physics Lab. Report TG 609, 1964
  • [6] N. Bazley, Lower bounds for eigenvalues, J. Math. Mech. 10 (1961), 289-308 MR 0128612
  • [7] J. B. Diaz, Upper and lower bounds on eigenvalues, in 8th Symposium in Applied Mathematics, A. M. S., pp. 53-58, New York, 1958 MR 0093907
  • [8] G. Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, Springer-Verlig, 1964 MR 0209639
  • [9] -, Lezioni sulle transformazioni lineari, Inst. Math. Univ. Trieste, 1954.
  • [10] S. H. Gould, Variational methods in eigenvalue problems, Univ. of Toronto Press, Toronto 1957 MR 0087019
  • [11] T. Kato, Quadratic forms in Hilbert space and asymptotic perturbation series, Univ. of California, lecture notes, Berkeley, Calif., 1955 MR 0073958
  • [12] L. E. Payne, Inequalities for eigenvalues of membranes and plates, J. Rat. Mech. Anal. 4 (1955), 517-529 MR 0070834
  • [13] A. Weinstein, Sur la stabilité des plaques encastrées, Compt. Rend. 200 (1935), 107-109
  • [14] -, Intermediate problem and the maximum-minimum theory of eigenvalues, J. Math. Mech. 12, 235-246, (1963) MR 0155083
  • [15] -, Some applications of the new maximum-minimum theory of eigenvalues, J. Math. Anal. Applic. 12 (1965), 58-64 MR 0182800
  • [16] -, A necessary and sufficient condition in the maximum-minimum theory of eigenvalues, studies in mathematical analysis and related topics. Stanford, Stanford Univ. Press, 1962 MR 0149657
  • [17] -, Bounds for eigenvalues and the method of intermediate problems, in proceedings of the international conference on partial differential equations and continuum mechanics, Madison, University of Wisconsin Press, 1961, pp. 39-53. MR 0126068
  • [18] L. E. Elsgolc, Calculus of variations, Addison-Wesley, Reading Mass., 1962 MR 0133032
  • [19] S. T. Kuroda, Finite dimensional perturbation and representation of the scattering operator, Pacific J. of Math. 13 (1963), 1305-1318 MR 0156210

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35J40

Retrieve articles in all journals with MSC: 35J40


Additional Information

DOI: https://doi.org/10.1090/qam/425349
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society