有界域上涉及临界增长含任意特征值的一类共振问题

A Class of Resonance Problems on Bounded Domains for Arbitrary Eigen-value,involving the Critial Sobolev Exponent

给出了半线性椭圆方程 -Δu=λu + ｜u｜2 - 2 u -f(x ,u) ,λ∈ [λ1 ,λk] ;-Δu=λu -γ(x ,u) +h(x) ,limu→∞γ(x ,u)｜u｜ =+∞ λ∈ [λ1 ,λk]的Dirichent问题的非平凡解的存在性定理等。

In this paper, existence theorems of non-trivial solution for a class of semilinear elliptic equations -Δu=λu+|u| 2*-2 u-f(x,u),λ∈\[λ 1,λ k\];-Δu=λu-γ(x,u)+h(x), lim u→∞γ(x,u)|u|=+∞ λ∈\[λ 1,λ k\]and so on, were given.