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

Weyl Anomalies of Strings in Temporal Gauge

We consider two-dimensional quantum gravity coupled to matter in the temporal gauge, using the Polyakov path integral. We show that the integration over the metric can be explicitly performed under some plausible assumptions. We also discuss that the critical dimensions in string theory may not be determined in the temporal gauge.Comment: 20 pages, RevTe

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