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

TL;DR

This paper proves that the previously assumed technical condition for the uniqueness of positive solutions in semilinear elliptic equations with double power nonlinearities is actually unnecessary, simplifying the understanding of solution uniqueness.

Contribution

The paper demonstrates that the additional condition for uniqueness, proposed in 1998, can be omitted, thus simplifying the criteria for positive solution uniqueness.

Findings

The uniqueness condition is unnecessary.

Simplified criteria for positive solutions.

Clarification of solution properties in elliptic equations.

Abstract

We consider uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities. The condition to assure the existence of positive solutions to these types of equations has long been known. On the other hand for uniqueness, quite technical additional condition is proposed by Ouyang and Shi in 1998. In the present paper we remark that this additional condition is unnecessary.