Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T00:25:28.367Z Has data issue: false hasContentIssue false
  • English
  • Français

Limit Point and Limit Circle Criteria for a Class of Singular Symmetric Differential Operators

Published online by Cambridge University Press:  20 November 2018

Robert L. Anderson
Robert L. Anderson*
Affiliation:
Deering Milliken Service Corporation, Spartanburg, South Carolina
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For certain classes of singular symmetric differential operators L of order 2n, this paper considers the problem of determining sufficient conditions for L to be of limit point type or of limit circle type. The operator discussed here is defined by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 905 - 914
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Anderson, R. L., Singular symmetric differential operators on a Hilbert Space of vector valued functions, Unpublished doctoral dissertation, The University of Tennessee, Knoxville, Tennessee, 1973.Google Scholar
2. Bellman, R., Stability theory of differential equations (Dover Publications, Inc., New York, 1969).Google Scholar
3. Coppel, W. A., Stability and asymptotic behavior of differential equations (D. C. Heath and Company, Boston, 1965).Google Scholar
4. Everitt, W. N., Some positive definite differential operators, J. London Math. Soc. 1-3 (1968), 465–473.Google Scholar
5. Everitt, W. N., On the limit-point classification of fourth-order differential equations, J. London Math. Soc. U (1969), 273–281.Google Scholar
6. Everitt, W. N. and Chandhuri, J., On the square of a formally self-adjoint expression, J. London Math. Soc. U (1969), 661–673.Google Scholar
7. Glazman, I. M., On the theory of singular differential operators, Uspekhi Mat. Nauk. 5, 0(40) (1950) 102–35,. (Russian).Google Scholar
8. Hinton, D., Limit point criteria for differential equations, Can. J. Math. 24 (1972), 293–305.Google Scholar
9. Hinton, D., Limit point criteria for positive definite fourth-order differential operators, to appear.Google Scholar
10. Lidskii, V. B., On the number of solutions with integrable square of the system y” + Py= \y, Doklady Akad. Nauk. SSSR (N.S.) 95 (1954), 217–220. (Russian).Google Scholar
11. Naimark, M. A., Linear differential operators, Part I (Ungar, New York, 1967).Google Scholar
12. Walker, P., Asymptotica of the solutions to [﹛ry“)’ —py'Y + qy = ay, J. Differential Equations 9 (1971), 108–132.Google Scholar
13. Walker, P., Deficiency indices of fourth-order singular differential operators, J. Differential Equations 9 (1971), 133–140.Google Scholar