Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T00:38:32.816Z Has data issue: false hasContentIssue false
  • English
  • Français

Limit circle criteria for fourth order differential operators with an oscillatory coefficient

Published online by Cambridge University Press:  20 January 2009

Ronald I. Becker
Ronald I. Becker
Affiliation:
Department of MathematicsUniversity of Cape Town7700 Rondebosch, Cape, Republic of South Africa
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.

A formally self-adjoint operator L is said to be of limit circle type at infinity if its highest order coefficients are zero-free and all solutions x of L(x) = 0 are square-integrable on [c, ∞) for some c. (We will drop “at infinity” in what follows.)

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 2 , June 1981 , pp. 105 - 117
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Atkinson, F. V., Asymptotic integration and the L 2-classification of squares of differential expressions, Quaestiones Mathematicae 1 (1976), 155–180.CrossRefGoogle Scholar
(2)Becker, R. I., Asymptotic expansions of second order linear differential equations having conditionally integrable coefficients, J. London Math. Soc. (2) 20 (1979), 472–484.CrossRefGoogle Scholar
(3)Becker, R. I., Asymptotic expansions of formally self-adjoint differential equations with conditionally integrable coefficients, Quart. J. Math. Oxford (2) 31 (1980), 49–64.CrossRefGoogle Scholar
(4)Becker, R. I., Limit circle criteria for 2n-th order differential operators, Proc. Edinburgh Math. Soc. 24 (1981), 59–72.CrossRefGoogle Scholar
(5)Coppel, W. A., Stability and Asymptotic Behavior of Differential Equations. (Heath, Boston, 1965).Google Scholar
(6)Eastham, M. S. P., Limit-circle differential expressions of the second order with an oscillating coefficient, Quart. J. Math. Oxford (2) 24 (1973), 257–263.CrossRefGoogle Scholar
(7)Eastham, M. S. P. and Thomson, M. L., On the limit-point, limit-circle classification of second-order differential equations, Quart. J. Math. Oxford (2) 24 (1973), 531–535.CrossRefGoogle Scholar
(8)Read, T. T., Perturbations of limit-circle expressions, Proc. Amer. Math. Soc., 56 (1976), 108–110.CrossRefGoogle Scholar