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The real solutions of a certain non-linear system of equations

Published online by Cambridge University Press:  24 October 2008

N. R. Lebovitz
N. R. Lebovitz
Affiliation:
Yerkes ObservatoryThe University of Chicago
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Extract

In a recent paper on the behaviour of a system of disk dynamos(1), a problem of a purely algebraic character arose. The problem is to find all the real solutions of the non-linear, inhomogeneous system of 2n equations

where x0 = xn and the parameter ρ is real and not zero, but otherwise arbitrary. The real solutions were correctly given in (1), but the proof that they are the only real solutions was incomplete. A different, and complete, proof is given here.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 503 - 506
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Lebovitz, N. R.Proc. Camb. Phil. Soc. 56 (1960), 154–73.CrossRefGoogle Scholar