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A Note on the Dirichlet Condition for Second-Order Differential Expressions

Published online by Cambridge University Press:  20 November 2018

W. N. Everitt
W. N. Everitt*
Affiliation:
University of Dundee, Dundee, Scotland
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Let M denote the formally symmetric, second-order differential expression given by, for suitably differentiable complex-valued functions ƒ,

The coefficients p and q are real-valued, Lebesgue measurable on the halfclosed, half-open interval [a, b) of the real line, with - ∞ < a < b ≦ ∞, and satisfy the basic conditions:

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 312 - 320
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Atkinson, F. V., Limit-n criteria of integral type, Proc. Royal Soc. Edinb. (A) 73 (1975), 167–198.Google Scholar
2. Everitt, W. N., A note on the self-adjoint domains of second-order differential equations. Quart. J. Math. (Oxford) (2) 14 (1963), 41–45.Google Scholar
3. Everitt, W. N., Qn tfog Umit-point classification of second-order differential operators, J. Lond. Math. Soc. 41 (1966), 531–44.Google Scholar
4. Everitt, W. N., On the strong limit-point condition of second-order differential expressions, Internation Conference on Differential Equations, (Academic Press, New York, 1975), 287–307.Google Scholar
5. Everitt, W. N., and Giertz, M., A Dirichlet type result for ordinary differential operators, Math. Ann. 203 (1973), 119–28.Google Scholar
6. Everitt, W. N., M. Giertz and McLeod, J. B., On the strong and weak limit-point classification of second-order differential expressions, Proc. London Math. Soc. (3) 29 (1974), 142–158.Google Scholar
7. Kalf, H., Remarks on some Dirichlet type results for semi-bounded Sturm-Liouville operators, Math. Ann. 210 (1974), 197–205.Google Scholar
8. Naimark, M. A., Linear differential operators : Part II (Ungar, New York, 1968).Google Scholar