关于带第一特征值 λ_1具Sobolev临界指数 2~* 的一类椭圆方程-Δu=λ_1u+|u|^(2^*-2) u+τ(x,u)(英文)

On the elliptic equations -Δu=λ_1u+|u|^(2^*-2)u+τ(x,u) with the first eigenvalue λ_1,involving the critical Sobolev exponent 2~*

给出了半线性椭圆方程 -Δu=λ1 u+|u|2 * - 2 u+τ( x,u)的 Dirichlet问题在对扰动项τ( x,u)增加适当条件后非平凡解的存在性定理 ,以及方程 -Δu=λu-|u|2 * - 2 u+h( x) ,λ∈ [λ1 ,λk](这里λk 是方程-Δu=λu的第 k个互不相等的特征值 )

We gave the existence theorem of non-trivial solution f or a class of semilinear elliptic equations -Δu=λ 1u+|u| 2 *-2 u+τ(x, u),under some conditions on τ(x,u), and considered the existence theorem of non-zero solution for a class of semilinear elliptic equations -Δu=λu-| u| 2 *-2 u+h(x),λ∈[λ 1,λ k], where λ k is the kth dist inct eigenvalue of the eigenvalue problem -Δu=λ 1u in H 1 0(Ω) and the critical Sobolev exponent 2 *=2NN-2.