Uniqueness of the positive solution for a class of semilinear elliptic systems

We prove the uniqueness of the positive radially symmetric solution to the following problem: {Δu+λvp1=0,x∈B1,Δv+λwp2=0,x∈B1,Δw+λup3=0,x∈B1,u=v=w=0,x∈∂B1, where pi>0(i=1,2,3) and B1B1 is the unit ball in RnRn.