具有Sobolev临界指数的非线性椭圆型方程解的存在性

Nortrivial Solution for Some Nonlinear Elliptic Equations with Critical Sobolev Exponennt

设ΩＲＮ（Ｎ＞２）是单位球，文中讨论了非线性椭圆型方程－Δｕ＝ａ（ｘ）｜ｕ｜２－２ｕ＋λｕ，ｘ∈Ωｕ＝０，ｘ∈Ω｛解的存在性，其中２＝２ＮＮ－２是Ｓｏｂｏｌｅｖ临界指数，λ为常数。在ａ（ｘ）的适当限制下，得到了上述问题的一个存在性结果。

The boundary value problems are considered: - Δ u=a(x)|u| 2 -2 u+λu,x∈Ω u=0,x∈Ω where ΩR N (N>2) is the unit ball, 2 =2NN-2 is the critical exponent for the Sololev embedding and λ is a real parameter. The existence of nontrivial solutions of the above problems are proved.