Uniqueness of Positive Solutions for Semilinear Neumann Problems in a Half Space

In this paper, we consider positive solutions of the following boundary Neumann problem in half space -Delta u = a(x)u - b(x)u(q) x is an element of T, partial derivative u/partial derivative n = 0, on partial derivative T, Where T = {x = (x(1), x(2),... x(N),) : x(N) > 0},(N >= 2), q is a constant greater than 1, a(x) and b(x) are continuous functions with b(x) positive on R-N and n is outward pointing unit normal vector of partial derivative T. Under suitable conditions, we show that this problem has only one positive solution.