Brown, Brian Malcolm and Reichel, W. 2004. Eigenvalues of the radially symmetric p-Laplacian in Rn. Journal of the London Mathematical Society 69 (3) , pp. 657-675. 10.1112/S002461070300512X |
Abstract
For the p-Laplacian p = div:(| |pâ€“2), p>1, the eigenvalue problem â€“p + q(|x|)||pâ€“2 = ||pâ€“2 in Rn is considered under the assumption of radial symmetry. For a first class of potentials q(r) as r at a sufficiently fast rate, the existence of a sequence of eigenvalues k if k is shown with eigenfunctions belonging to Lp(Rn). In the case p=2, this corresponds to Weyl's limit point theory. For a second class of power-like potentials q(r)â€“ as r at a sufficiently fast rate, it is shown that, under an additional boundary condition at r=, which generalizes the Lagrange bracket, there exists a doubly infinite sequence of eigenvalues k with k Â± if kÂ±. In this case, every solution of the initial value problem belongs to Lp(Rn). For p=2, this situation corresponds to Weyl's limit circle theory.
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | Computer Science & Informatics |
Publisher: | London Mathematical Society |
ISSN: | 0024-6107 |
Last Modified: | 04 Jun 2017 01:41 |
URI: | http://orca.cf.ac.uk/id/eprint/1767 |
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