具有Sobolev临界指数的双调和方程解的存在性

Existence of Nontrivial Solution for Biharmonic Problems Involving Critical Sobolev Exponent

设ΩRN(N≥5)是一个有界光滑区域,且0∈Ω,0≤s≤4,2*=(2N)/(N-4)是Sobolev临界指数,f(x),g(x)是已给函数.借助变分方法,本文在f(x),g(x),μ,λ的一定条件下,讨论了临界非齐问题Δ2u-μu/|x|s=|u|2*-2+λμf(x)+g(x)满足Dirichlet边界条件的解的存在性.

Let ΩRN（N≥5） be a smooth bound domain such that 0∈Ω,0≤s≤4.2＊=（2N）/（N-4） is the critical Sobolev exponent,and f（x）,g（x） are given functions.By using the variational methods,the paper proves the existence of solutions for the singular critical in the nonhomogeneous problem Δ2u-μu/｜x｜S=｜u｜2＊-2u＋λuf（x）＋g（x） with Dirichlet boundary condition on Ω under some assumptions on f（x） g（x）,μ and λ.