Eigenvalues of the radially symmetric p-Laplacian in Rn

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591 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

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Abstract

For the p-Laplacian p = div:(| |p–2), p>1, the eigenvalue problem –p + q(|x|)||p–2 = ||p–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)– 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 ± if k±. 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
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Publisher:	London Mathematical Society
ISSN:	0024-6107
Last Modified:	17 Oct 2022 09:00
URI:	https://orca.cardiff.ac.uk/id/eprint/1767

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