Abstract and Applied Analysis
Volume 2003 (2003), Issue 13, Pages 743-755
doi:10.1155/S1085337503303069

On the A-Laplacian

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.