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VI.—On Solvability of Some Two-Parameter Eigenvalue Problems in Hilbert Space

Published online by Cambridge University Press:  14 February 2012

Z. Bohte
Z. Bohte
Affiliation:
University of Surrey, London.
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Synopsis

This paper studies two particular cases of the general 2-parameter eigenvalue problem namely

where A, B, B1, B2, C, C1, C2 are self-adjoint operators in Hilbert space, all except A being bounded. The disposable parameters λ and μ have to be determined so that the equations have non-trivial solutions x, y.

On the assumption that the solution is known for ∊ = o, solutions are constructed in the form of series for λ, μ, x, y as power series in ∊ with finite radius of convergence.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 68 , Issue 1 , 1968 , pp. 83 - 93
Copyright
Copyright © Royal Society of Edinburgh 1968

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References

References to Literature

Arscott, F. M., 1964. “Two-parameter eigenvalue problems in differential equations”, Proc. Lond. Math. Soc., 14, 459–470.CrossRefGoogle Scholar
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