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26.—The Strong Limit-2 Case of Fourth-order Differential Equations

Published online by Cambridge University Press:  14 February 2012

V. Krishna Kumar
V. Krishna Kumar
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur, India†
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Synopsis

The fourth-order equation considered is

Conditions are given on the coefficients r, p and q which ensure that this differential equation (*) is in the strong limit-2 case at ∞, i.e. is limit-2 at ∞. This implies that (*) has exactly two linearly independent solutions which are in the integrable-square space ℒ2(0, ∞) for all complex numbers λ with im [λ] ≠ 0. Additionally the conditions imply that self-adjoint operators generated by M[·] in ℒ2(0, ∞) are semi-bounded below. The results obtained are applied to the case when the coefficients r, p and q are powers of x ∈ [0, ∞).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 71 , Issue 4 , 1974 , pp. 297 - 304
Copyright
Copyright © Royal Society of Edinburgh 1974

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References

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