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Asymptotic decay of the solution of a second-order elliptic equation in an unbounded domain. Applications to the spectral properties of a Hamiltonian

Published online by Cambridge University Press:  14 February 2012

C. Bardos  and
M. Merigot
C. Bardos
Affiliation:
I.M.S.P., Département de Mathématiques, Université de Nice
M. Merigot
Affiliation:
I.M.S.P., Département de Mathématiques, Université de Nice
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Synopsis

In an unbounded domain Ω we study the asymptotic decay (for | x |→∞) of functions u ∊ L2(Ω) which are solutions of the following problem –Δu + cu = 0. c denotes a strictly positive function. Upper bounds are easily found via the maximum principle. When c is rotationally invariant lower bounds are obtained via asymptotic expansion. In the general case we use a method of ‘commutation’ of operators. In particular we consider the case where . Applications to the asymptotic decay of the bound states of a Hamiltonian are given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 4 , 1977 , pp. 323 - 344
Copyright
Copyright © Royal Society of Edinburgh 1977

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