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On the deficiency indices of a fourth order singular differential operator

Published online by Cambridge University Press:  14 November 2011

Alastair D. Wood
Alastair D. Wood
Affiliation:
Department of Mathematics, Cranfield Institute of Technology, Bedford, England
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Synopsis

We consider the operator L[y] = y(4) + ((ax2 + bx + c)y′)′ + dy on the half-line [0, ∞). This paper shows that the deficiency indices are independent of the real numbers b, c and d when a ≠ 0. They depend only on the sign of a and are (2,2) if a < 0 and (3, 3) if a > 0. In the case a =0 the sign of b must be considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 173 - 176
Copyright
Copyright © Royal Society of Edinburgh 1979

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