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Strong limit-point and Dirichlet criteria for ordinary differential expressions of order 2n

Published online by Cambridge University Press:  14 February 2012

Don Hinton
Don Hinton
Affiliation:
University of Tennessee, Knoxville
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Synopsis

Conditions are given which ensure that a weighted 2nth order ordinary differential equation on a half-line satisfy the strong limit-point and Dirichlet conditions. Perturbation terms are permitted which either satisfy certain pointwise bounds or integral type bounds. Not all of the coefficients of the equation are required to be non-negative.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 4 , 1977 , pp. 301 - 310
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Akhiezer, N. I. and Glazman, I. M.. Theory of linear operators in Hilbert space, II (New York: Ungar, 1963).Google Scholar
2Anderson, L. and Lazer, A.. On the solutions of linear selfadjoint differential equations. Trans. Amer. Math. Soc. 152 (1970), 519–530.CrossRefGoogle Scholar
3Atkinson, F. V.. Limit-n criteria of integral type. Proc. Roy. Soc. Edinburgh Sect. A 73 (1975), 167–198.CrossRefGoogle Scholar
4Brown, B. M. and Evans, W. D.. On the limit-point and strong limit-point classification of 2nth order differential expressions with wildly oscillating coefficients. Math. Z. 134 (1973), 351–368.CrossRefGoogle Scholar
5Everitt, W. N.. A note on the Dirichlet condition for second-order differential expressions. Canad. J. Math. 28 (1976), 312–320.CrossRefGoogle Scholar
6Everitt, W. N. and Giertz, M.. A Dirichlet type result for ordinary differential operators. Math. Ann. 203 (1973), 119–128.CrossRefGoogle Scholar
7Everitt, W. N., Hinton, D. B. and Wong, J. S. W.On the strong limit-n classification of linear ordinary differential expressions of order 2n. Proc. London Math. Soc. 29 (1974), 351–367.CrossRefGoogle Scholar
8Everitt, W. N., Giertz, M. and McLeod, J. B.. On the strong and weak limit-point classification of second-order differential expressions. Proc. London Math. Soc. 29 (1974), 142–158.CrossRefGoogle Scholar
9Everitt, W. N., Giertz, M. and Weidmann, J.. Some remarks on a separation and limit-point criterion of second-order ordinary differential expression. Math. Ann. 200 (1973), 335–346.CrossRefGoogle Scholar
10Hinton, D. B.. Limit point criteria for differential equations. Canad. J. Math. 24 (1972), 293–305.CrossRefGoogle Scholar
11Hinton, D. B.. Limit point criteria for differential equations, II. Canad. J. Math. 26 (1974), 340–351.CrossRefGoogle Scholar
12Hinton, D. B.. Limit-point limit-circle criteria for (py′)′ + qy = λky. Lecture Notes in Mathematics 415 (Berlin: Springer, 1974).Google Scholar
13Kalf, H.. Remarks on some Dirichlet type results for semibounded Sturm-Liouville operators. Math. Ann. 210 (1974), 197–205.CrossRefGoogle Scholar
14Kumar, K.. The strong limit-2 case of fourth-order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 71 (1974), 297–304.Google Scholar
15Kumar, K.. On the strong limit-point classification of fourth-order differential expressions with complex coefficients. J. London Math. Soc. 12 (1976), 287–298.CrossRefGoogle Scholar