Uniqueness of positive radial solutions of Δu+f(u)=0Δu+f(u)=0 in RNRN, N≥2N≥2

We study the uniqueness of radially symmetric ground states for the semilinear elliptic partial differential equation Δu+f(u)=0inRN,N≥2. Assuming that F(t)=∫0tf(s)ds is negative in (0,u1)(0,u1) and positive in (u1,ū), we obtain the uniqueness of nonnegative solutions with u(0)=supu∈(0,ū) in the case where S(u)=uf′(u)/f(u)S(u)=uf′(u)/f(u) is monotonically decreasing in [u1,ū).