On theA-Laplacian

[摘要] We prove, for Orlicz spacesLA(ℝN)suchthatAsatisfies theΔ2condition, the nonresolvability of theA-Laplacian equationΔAu+h=0onℝN, where∫h≠0, ifℝNisA-parabolic. For a large class of Orlicz spaces including Lebesgue spacesLp(p>1), we also prove that the same equation, with any bounded measurable functionhwith compact support, has a solution with gradient inLA(ℝN)ifℝNisA-hyperbolic.

[学科分类] 数学（综合）