Title: Nontrivial solution for a semilinear elliptic equation in unbounded domain with critical Sobolev exponent
Abstract: where Ω is an unbounded domains with smooth boundary in R , 2∗ = 2N/ (N − 2), a(x) ∈C1(Ω) satisfies the following conditions: (A1) a ∈ LN/2(Ω). (A2) Ω− = {x ∈Ω | a(x) 0 such that B(θ,4δ)⊂⊂Ω−. When Ω is a bounded domain with smooth boundary in R (N 5), similar problem has been studied by many mathematicians; for example, in [3], Brezis and Nirenberg studied problem (P). In [4], Capozzi et al. prove that when Ω