Uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities

We consider semilinear elliptic equations with double power nonlineaities. The condition to assure the existence of positive solutions is well-known. In the present paper, we remark that the additional condition to assure uniqueness proposed by Ouyang and Shi is unnecessary

On the maximum value of ground states for the scalar field equation with double power nonlinearity

We evaluate the maximum value of the unique positive solution to semilinear elliptic equations with double power nonlinearities. It is known that a positive solution to this problem exists under some condition.Moreover, Ouyang and Shi in 1998 found that the solution is unique under the same condition. In the present paper we investigate the maximum value of the solution. The key idea is to examine the function defined from the nonlinearity, which arises from the well-known Pohozaev identity.Comment: 8 page

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)

On semilinear elliptic equations with nonlocal nonlinearity

We consider the problem 1, k > 0 are constants. We classify the existence of all possible ositive solutions to this problem