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
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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
---, II, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 594–601
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---, Methods for lower bounds to frequencies of continuous elastic systems, John Hopkins Univ. Applied Physics Lab. Report TG 609, 1964
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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
---, II, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 594–601
---, Approximation methods for eigenvalues of completely continuous symmetric operators, in Proc. Symp. Spectral Theory and Differential Problems, Oklahoma State Univ., Stillwater, Okla., 1951
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)
---, Methods for lower bounds to frequencies of continuous elastic systems, John Hopkins Univ. Applied Physics Lab. Report TG 609, 1964
N. Bazley, Lower bounds for eigenvalues, J. Math. Mech. 10 (1961), 289–308
J. B. Diaz, Upper and lower bounds on eigenvalues, in 8th Symposium in Applied Mathematics, A. M. S., pp. 53–58, New York, 1958
G. Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, Springer-Verlig, 1964
---, Lezioni sulle transformazioni lineari, Inst. Math. Univ. Trieste, 1954.
S. H. Gould, Variational methods in eigenvalue problems, Univ. of Toronto Press, Toronto 1957
T. Kato, Quadratic forms in Hilbert space and asymptotic perturbation series, Univ. of California, lecture notes, Berkeley, Calif., 1955
L. E. Payne, Inequalities for eigenvalues of membranes and plates, J. Rat. Mech. Anal. 4 (1955), 517–529
A. Weinstein, Sur la stabilité des plaques encastrées, Compt. Rend. 200 (1935), 107–109
---, Intermediate problem and the maximum-minimum theory of eigenvalues, J. Math. Mech. 12, 235–246, (1963)
---, Some applications of the new maximum-minimum theory of eigenvalues, J. Math. Anal. Applic. 12 (1965), 58–64
---, A necessary and sufficient condition in the maximum-minimum theory of eigenvalues, studies in mathematical analysis and related topics. Stanford, Stanford Univ. Press, 1962
---, 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.
L. E. Elsgolc, Calculus of variations, Addison-Wesley, Reading Mass., 1962
S. T. Kuroda, Finite dimensional perturbation and representation of the scattering operator, Pacific J. of Math. 13 (1963), 1305–1318
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© Copyright 1974
American Mathematical Society
