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Abstract and Applied Analysis
Volume 2003 (2003), Issue 13, Pages 743-755

On the A-Laplacian

Département de Mathématiques École Normale Supérieure, Ben Souda, Fès BP 5206, Morocco

Received 25 January 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove, for Orlicz spaces LA(N) such that A satisfies the Δ2 condition, the nonresolvability of the A-Laplacian equation ΔAu+h=0 on N, where h0, if N is A-parabolic. For a large class of Orlicz spaces including Lebesgue spaces Lp (p>1), we also prove that the same equation, with any bounded measurable function h with compact support, has a solution with gradient in LA(N) if N is A-hyperbolic.