关于变奇异指数的各向异性$p$-Laplace方程

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations Pub Date : 2021-04-08 DOI:10.57262/ade026-1112-535

K. Bal, Prashanta Garain, T. Mukherjee

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引用次数: 11

摘要

 −∆H、 pu=Ω中的λf（x）uq（x）+g（u），Ω中的u>0，在？Ω上的u=0，假设Ω是R中的有界光滑域，其中p，N≥2，λ>0和0本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On an Anisotropic $p$-Laplace equation with variable singular exponent

 −∆H,pu = λf(x) uq(x) + g(u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, under the assumption Ω is a bounded smooth domain in R with p,N ≥ 2, λ > 0 and 0 < q ∈ C(Ω̄). For the purely singular case that is g ≡ 0, we proved existence and uniqueness of solution. We also demonstrate the existence of multiple solution to (P ) provided f ≡ 1 and g(u) = u for r ∈ (p− 1, p − 1).