A remark on the uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities

We consider the uniqueness of positive solutions to 1, a positive solution to (1) exists if and only f ω 2 (0, ωp), where ωp := p + 1)2 . We deduce the uniqueness in the ase where ω is close to ωp, from the argument in the classical paper by eletier and Serrin [9], thereby recovering a part of the uniqueness result f Ouyang and Shi [8] for all ω 2 (0, ωp)