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

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