Bibliography
Adams, R. A., Compact Sobolev imbeddings for unbounded domains with discrete boundaries. J. of Math. Anal, and Appl. 24, No. 2 (1968).
Adams, R. A., Capacity and compact imbeddings. J. Math. Mech. 19, No. 10 (1970).
Agmon, S., Lectures on Elliptic Boundary Value Problems. Princeton: Van Nostrand 1965.
Clark, C., An embedding theorem for function spaces. Pacific J. Math. 19 (1966).
Clark, C., Inequalities of Poincaré type and applications to singular elliptic differential operators. Math. Ann. 176 (1968).
Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. I, II. New York: Wiley 1953.
Hersch, J., Erweiterte Symmetrieeigenschaften von Lösungen gewisser linearer Rand- und Eigenwertprobleme. J. Reine Angew. Math. 218 (1965).
Leis, R., Zur Monotonie der Eigenwerte selbstadjungierter elliptischer Differentialgleichungen. Math. Z. 96 (1967).
Mikhlin, S. G., The Problem of the Minimum of a Quadratic Functional. Holden-Day 1965.
Pederson, R. N., On the unique continuation theorem for certain second and fourth order elliptic equations. Comm. Pure Appl. Math. 11 (1958).
Persson, A., Bounds for the discrete part of the spectrum of a semi-bounded Schrödinger operator. Math. Scand. 8 (1960).
Protter, M. H., Unique continuation for elliptic equations. Trans. Amer. Math. Soc. 95 (1960).
Stenger, W., On the variational principles for eigenvalues for a class of unbounded operators. J. Math. Mech. 17, No. 7 (1968).
Welsh, W., Properties of Eigenvalues of Singular Second Order Elliptic Operators. Thesis, U.B.C. 1970.
Author information
Authors and Affiliations
Additional information
Communicated by M. M. Schiffer
Rights and permissions
About this article
Cite this article
Welsh, W. Monotonicity for eigenvalues of the Schrödinger operator on unbounded domains. Arch. Rational Mech. Anal. 49, 129–136 (1972). https://doi.org/10.1007/BF00281414
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00281414