无界域上含临界指数的P-Laplace方程的非平凡解

The Nontrivial Solutions of P-Laplace Equation Involving Critical Sobolev Exponent in Unbounded Domains

给出无界域上含临界指数的P-Laplace方程:(2≤p<N,p=NP/(N-P))的非平凡广义解的存在性结果。

It is given that the existence of solutions of P-Laplace equation involving critical Sobolev exponent in unbounded domains: -sum from i=1 to N (a/(ax_i))(|Vu|^(p-2)(au)/(ax_i))+a(x)|u|^(p-2)=|u|^(p^*-2)u+f(x,u),u∈W^(1,p)(R^N) wherc 2<P<N, P~*=NP/(N-P).