On the A -Laplacian

Noureddine Aïssaoui

Abstract and Applied Analysis, 2003, vol. 2003, 1-13

Abstract:

We prove, for Orlicz spaces L A ( ℝ N ) such that A satisfies the Δ 2 condition, the nonresolvability of the A -Laplacian equation Δ A u + h = 0 on ℝ N , where ∫ h ≠ 0 , if ℝ N is A -parabolic. For a large class of Orlicz spaces including Lebesgue spaces L p ( p > 1 ), we also prove that the same equation, with any bounded measurable function h with compact support, has a solution with gradient in L A ( ℝ N ) if ℝ N is A -hyperbolic.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:414310

DOI: 10.1155/S1085337503303069

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