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.