一类带有Hardy项和Sobolev-Hardy临界指数椭圆方程的非平凡解

摘要

It was discussed a class of elliptic equations involving Hardy terms and Sobolev-Hardy critical exponents {-△u-μ+h(x)/|x|2u=|u|2*(s)-2-|x|su+λ|u|q-2u,x∈Ω;u=0,x∈(δ)Ω The existence of nontrivial solutions was proved via variational methods and delicate estimates, where Ω?Rn (N≥3) was an bounded domain with smooth boundary and containing the origin 0,γ>0,μ,∈R,0≤s<2.%研究了一类带有Hardy项和Sobolev-Hardy临界指数的椭圆方程{-△u-μ+h(x)/|x|2u=|u|2*(s)-2-|x|su+λ|u|q-2u,x∈Ω;u=0,x∈(δ)Ω.通过运用变分方法和精确估计得到了非平凡解u ∈ D1,2(Ω)的存在性.其中:Ω(C)RN(N≥3)是一个有界光滑区域,0∈Ω,λ＞0,μ∈R,0≤s＜2.