On the existence of a positive solution for a semilinear elliptic equation in the upper half space - Chen Shaowei; Li Yongqing (Abstract and Applied Analysis)
We show the existence of a nontrivial solution to the semilinear elliptic equation −Δu+u=b(x)|u|p−2u, u>0,  u∈H01(ℝ+N) under some suitable conditions.