References
Weinstein, A.: Sur la stabilité des plaques encastrées, C. R.200, 107–109 (1935).
Weinstein, A.: J. London Math. Soc.10, 184 (1935).
Weinstein, A.: Mémorial des Sciences Mathématiques, fasc. 88. Paris: Gauthier-Villars 1937.
Gould, S. H.: Variational Methods in Eigenvalue Problems. Toronto: Univ. of Toronto Press 1957. A second enlarged edition of the book ofS. H. Gould is in preparation.
Weyl, H.: Ramifications, Old and New, of the Eigenvalue Problem. Bull. Amer. Math. Soc.46, 115–139 (1950).
Diaz, J. B.: Upper and Lower Bounds for Eigenvalues, Proceedings of the Eighth Symposium on Applied Mathematics. New York: American Mathematical Society 1958, pp. 53–78.
Weinstein, A.: Bounds for Eigenvalues and the Method of Intermediate Problems, Proceedings of the International Conference on Partial Differential Equations and Continuum Mechanics. Madison: Univ. Wisconsin Press 1961, pp. 39–53.
Velte, W.: Über ein Stabilitätskriterium der Hydrodynamik. Arch. for Rat. Mech. and Anal.9, 9–20 (1962).
Weinstein, A.: On the Decomposition of a Hilbert Space by its Harmonic Subspace. Amer. J. of Math.53, 615–618 (1941).
Weinstein, A.: A Necessary and Sufficient Condition in the Maximum-Minimum Theory of Eigenvalues, Studies in Mathematical Analysis and Related Topics. Stanford: Stanford Univ. Press 1962.
Payne, L. E.: Inequalities for Eigenvalues of Membranes and Plates. J. Rat. Mech. and Anal.4, 517–529 (1955).
Colautti, M. P.: Su un teorema di completezza connesso al metodo di Weinstein per il calcolo degli autovalori. Atti. Accad. Torino97, 1–21 (1962).
Aronszajn, N.: Approximation Methods for Eigenvalues of Completely Continuous Symmetric Operators, Proceedings of the Symposium on Spectral Theory and Differential Problems. Stillwater, Oklahoma, 1951.
Bazley, N. W.: Lower Bounds for Eigenvalues with Application to the Helium Atom. Nat. Acad. Sci.45, 850–853 (1959).
Bazley, N. W.: Lower Bounds for Eigenvalues. J. Math. and Mech.10, 289–308 (1961).
Bazley, N. W.: Lower Bounds for Eigenvalues with Application to the Helium Atom. Phys. Rev.120, 144–149 (1960).
Bazley, N. W., andD. W. Fox: Lower Bounds for Eigenvalues of Schrödinger's Equation. Phys. Rev.124, 483–492 (1961).
Bazley, N. W., andD. W. Fox: A Procedure for Estimating Eigenvalues. J. Math. Phys.3, 469–471 (1962).
Bazley, N. W., andD. W. Fox: Lower Bounds to Eigenvalues Using Operator Decompositions of the formB *B. Arch. for Rat. Mech. and Anal.10, 352–360 (1962).
Weinberger, H. F.: A Theory of Lower Bounds for Eigenvalues (Tech. Note BN-183). Institute for Fluid Dynamics and Applied Mathematics, Univ. of Maryland, 1959.
Bazley, N. W., andD. W. Fox: Truncations in the Method of Intermediate Problems for Lower Bounds to Eigenvalues. J. Res. Nat. Bur. Standards65B, 105–111 (1961).
Collatz, L.: Eigenwertprobleme und ihre Numerische Behandlung. Chelsea Publishing Co. 1948.
Aronszajn, N.: Rayleigh-Ritz and A. Weinstein Methods for Approximation of Eigenvalues, I, II. Proc. Nat. Acad. Sci.34, 474–480, 594–601 (1948).
Fichera, G.: Trasformazioni Lineari, 3d ed., Veschi, Roma (1962).
Svirskii, I. V.: Bull. Kazan, Ac. Sc. USSR3, 59–86 (1953).
Savinova, L. T.: Jour. Numerical Math.1, 714–719 (1961). This paper refers to the russian book ofS. G. Mikhlin, Variational Methods, Moscow (1959). The german translation used a previous edition of 1957.
Author information
Authors and Affiliations
Additional information
This research was supported in part by AFOSR Grant 62-454. Institute for Fluid Dynamics and Applied Mathematics University of Maryland College Park, Maryland.
Rights and permissions
About this article
Cite this article
Weinstein, A. On the Sturm-Liouville theory and the eigenvalues of intermediate problems. Numer. Math. 5, 238–245 (1963). https://doi.org/10.1007/BF01385895
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01385895