On the A‐Laplacian

Noureddine Aïssaoui

Abstract and Applied Analysis, 2003, vol. 2003, issue 13, 743-755

Abstract: We prove, for Orlicz spaces LA(ℝN) such that A satisfies the Δ2 condition, the nonresolvability of the A‐Laplacian equation ΔAu + h = 0 on ℝN, where ∫h ≠ 0, if ℝN 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(ℝN) if ℝN is A‐hyperbolic.

Date: 2003
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https://doi.org/10.1155/S1085337503303069

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:13:p:743-755

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