期刊论文

Existence of two weak solutions for biharmonic equations with the Hardy-Sobolev critical exponent and non-homogeneous perturbation term

中文

中国科学：数学

1674-7216

2019

49

12

1813-1844

10.1360/N012018-00250

国家自然科学基金(批准号:11771166)资助项目。

本校为第一机构

本文用变分方法研究如下RN 中包含 0的有界光滑区域Ω上带非齐次扰动项和 Hardy奇异项及 Sobolev临界指数项的非线性双调和问题:{△2u-λu/|x|s=|u|2**-2u+f(x),x∈Ω,u=(σ)u/(σ)n=0,x∈(σ)Ω(*)的非平凡解的存在性,其中 n 是(σ)Ω的单位外法向量,λ∈R,0≤s≤4,N≥5,且 2**=2N/N-4是H20(Ω)嵌入到 LP(Ω)的 Sobolev 临界指数,△2是重调和算子,f∈H-20(Ω).本文在f的范数适当小且相关参数满足适当的条件时证明(*)至少有两个非平凡解.本文的主要结果将 Tarantello(1992)关于调和方程的结果推广到了双调和方程,同时也将 Deng和 Wang(1999)的结果推广到了含 Hardy奇异项的情形,更重要的是本文考...

In this paper, we use the variational method to study the following nonlinear biharmonic elliptic problems involving a Hardy singular term and the Sobolev critical exponent and non-homogeneous term, where Ω ⊂ R~N is a bounded smooth domain containing 0, λ ∈ R, 0 ≤ s ≤ 4, N ≥ 5, n denotes the unit outward normal vector of ∂Ω, 2 ∗∗ = 2N/N – 4 is the critical Sobolev exponent for the embedding H_0~2(Ω), → L~p (Ω), and f ∈ H_0~(–2)(Ω). Under suitable assumptions on the parameters, we prove that the problem ( ∗ ) possesses at leas...