Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-15T10:59:48.254Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimate of the number of eigenvalues for an operator of Schrödinger type

Published online by Cambridge University Press:  14 November 2011

J. Fleckinger
J. Fleckinger
Affiliation:
Departement de Mathématiques, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France
Get access Rights & Permissions [Opens in a new window]

Synopsis

We obtain an asymptotic estimate for the number of eigenvalues less than λ of an operator of Schrödinger type

defined on an unbounded domain.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 3-4 , 1981 , pp. 355 - 361
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Courant, R and Hilbert, D.. Methods of mathematical physics (New York: Interscience, 1953).Google Scholar
2Fleckinger, J. Estimation des valeurs propres d'operateurs elliptiques sur des ouverts non bornés. Ann. Fac. Sci. Toulouse 12 (1980), 157–180.CrossRefGoogle Scholar
3Fleckinger, J.. Repartition des valeurs propres d'operateurs de type Schrödinger. C. R. Acad. Sci. Paris 292 (1981), 359–361.Google Scholar
4Metivier, G.. Valeurs propres de problèmes aux limites elliptiques irréguliers. Bull. Soc. Math. France Mém. 51–52 (1977), 125–219.CrossRefGoogle Scholar
5Lai, Pham The. Comportement asymptotique des valeurs propres d'une classe d'opérateur de type ‘Schrödinger’. J. Math. Kyoto Univ. 18 (1978), 353–375.Google Scholar
6Reed, M. and Simon, B.. Mathematical Physics (New York: Academic Press, 1978).Google Scholar
7Robert, D.. Propriétés spectrales d'opérateurs différentials (Thèse Univ. Nantes, 1977).Google Scholar
8Rozenbljum, G. V.. Asymptotics of the eigenvalues of the Schrödinger operator. Math. USSR-Sb. 22 (1974), 349–371.CrossRefGoogle Scholar
9Rozenbljum, G. V.. Asymptotics of the eigenvalues of the Schrödinger operator. Problemy Matematiceskogo Analiza 5 (1975), 152–166. (Russian)Google Scholar
10Titchmarsh, E.. Eigenfunction expansions, part 2 (Oxford Univ. Press, 1958).Google Scholar