R^N上临界增长的椭圆方程无穷多解的存在性

Existence of Infinitely Many Solutions on a Class of Elliptic Equations in R_N

本文证明了RN上的拟线性椭圆型方程-div（|Du|p-2Du）+|u|p-2u=λ（x）·|u|α-2u+a（x）|u|s-2u+b（x）|u|p＊-2u在W1,p（RN）中无穷多解的存在性,其中N≥3,2≤p<N,1<α<p<s<p＊=Np/N-p.

This paper gives the result of existence of infinitely many solutions on quasi-linear elliptic equation -div[|Du|p-2Du] +|u|p-2u=λ(x)|u|α-2u+a(x)|u|s-2u+a(x)|u|p*-2u in W1,P(RN), where N≥3, 2≤p<N, 1<α<p<s<p* =Np/N-p.