给出了半线性椭圆方程-Δu=λ1u+|u|2*-2u+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*-2u+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)的非零解的存在性定理.%We gave the existence theorem of non-trivial solution for a class of semilinear elliptic equations -Δu=λ1u+|u|2*-2u+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*-2u+h(x),λ∈[λ1,λk], where λk is the kth distinct eigenvalue of the eigenvalue problem -Δu=λ1u in H10(Ω) and the critical Sobolev exponent 2*=(2N)/(N-2).
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