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The number of Dirichlet solutions of a fourth order differential equation

Published online by Cambridge University Press:  14 November 2011

Thomas T. Read
Thomas T. Read
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225, U.S.A.
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Synopsis

It is shown that the equation (p2y”)”–(p1y’)’+ p0y = 0 has exactly two linearly independent solutions on [0,∞) with finite Dirichlet integral when the coefficients are nonnegative and p2 satisfies a condition which includes all nondecreasing functions. An inequality for the Dirichlet form is derived and used to extend characterizations of the domains of certain self-adjoint operations associated with the differential expression to arbitrary symmetric boundary conditions at 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 233 - 239
Copyright
Copyright © Royal Society of Edinburgh 1982

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References

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