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This work deals with the nonexistence of solutions of the semilinear elliptic equation -Δu = a(x)|u| p  in ℝ N  +  = { x = ( x 1  , . . . , x N ) ∈ ℝ N  : x N  &gt; 0 ) , with the boundary conditionon ∂ℝ N  +   = {(xʹ, 0) : xʹ ∈ ℝ N-1 }, where a(x) ≥ 0, b(xʹ) ≥ 0, p &gt; 1 and q &gt; 1. We are also concerned with a nonexistence result for the system -Δu i  = a i (x)|u i+1 | pi , x ∈ ℝ N  +  , 1 ≤ i ≤ m, u m+1  = u 1  withon ∂ℝ N  +  , where a i (x) ≥ 0 and p i  &gt; 1.

Absence of Solutions for Some Elliptic Equations and Systems in Half-Space with Nonlinear Neumann Boundary Conditions