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Ordinary and Partial Differential Equations pp 184–187Cite as

On second-order differential operators of limit-circle type

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 415))

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References

  1. R. Bellman, "A stability property of solutions of linear differential equations", Duke Math. J., 11(1944), 513–516.

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  2. N. Dunford and J.T. Schwartz, Linear operators; part II: Spectral theory (Interscience, New York, 1963).

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  3. M.S.P. Eastham, "Limit-circle differential expressions of the second order with an oscillating coefficient", Quart. J. Math. Oxford (2) 24 (1973), 257–263.

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  4. S. Halvorsen, "On the quadratic integrability of solutions of d2x/dt2+f(t)x=O" Math. Scand., 14(1964), 111–119.

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  5. I. Knowles, "On a limit-circle criterion for second-order differential operators", Quart. J. Math. Oxford (2), 24(1973), 451–455.

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  6. N.P. Kupcov, "Conditions of non-selfadjointness of a second order linear differential operator", Dokl. Akad. Nauk, 138 (1961), 767–770.

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  7. I.A. Pavlyuk, "Necessary and sufficient conditions for boundedness in the space L 2 [O, ∞) for solutions of a class of linear differential equations of second-order", Dopovidi Akad. Nauk Ukrain. RSR, 1960, 156–158.

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Authors
  1. Ian Knowles
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B. D. Sleeman I. M. Michael

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© 1974 Springer-Verlag

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Knowles, I. (1974). On second-order differential operators of limit-circle type. In: Sleeman, B.D., Michael, I.M. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065527

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  • DOI: https://doi.org/10.1007/BFb0065527

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06959-1

  • Online ISBN: 978-3-540-37264-6

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