带有临界Sobolev-Hardy指标椭圆问题的径向解(英文)

Radial Solutions for Elliptic Problems with Critical Sobolev-Hardy Exponents

设ΩcRN是球心在原点半径为R的球形区域,N≥3,0≤s<2,2*(s):=2(NN--2s),μ≥0,λ>0.运用变分方法和分析技巧,证明了带有Dirichlet边界条件的奇异临界问题-Δu-μxu 2=u 2x*(ss)-2u+λu的无穷多个径向解的存在性.这些解都带有不同个数的节点.

Let ΩRN be a ball centered at the origin with radius R>0,N≥3,0≤s<2,2*(s):=2(N-s)N-2,μ≥0 and λ>0.By applying the variational methods and analytic techniques,we prove the existence of infinitely many radial solutions for the singular critical problem -Δu-μu|x|2=|u|2*(s)-2|x|su+λu with Dirichlet boundary condition on Ω.Such solutions are characterized by the number of their nodes.