一类几乎临界增长方程解的存在性

Existence of Solution for an Equation with Slightly Critical Growth

运用变分方法及Hardy不等式讨论了下列半线性椭圆方程:-△u-μu/x2=u2*-1-ε+u,x∈Ω,其中该方程满足条件u>0,x∈Ω和u=0,x∈Ω,并且-∞<μ<■=[N-2/2]2,2*=2N/N-2,N≥3,ΩRN是包含0的有界光滑区域;当ε是小参数时可至少获得该方程的一个解。

A class special elliptic equation is discussed with strong singular item and involving critical Sobolev exponents by variational method in PDE and Hardy inequality：-△u-μ u/x^2=u^2^＊-1-g ＋u,x∈Ω,which is satisfied u〉0,x∈Ωand u=0,x∈ЭΩ,and slso-∞〈μ〈μ〈[N-2/2]^2,2^＊=2N/N-2,N≥3,Ω（∩→）R^N is a bound smooth domain which contains zero. As e is a small parameter, the existence of at least one solution of the equation is obtained.