Uniqueness and Liouville type results for radial solutions of some classes of k-Hessian equations

Abstract

We establish a uniqueness theorem and a Liouville type result for positive radial solutions of some classes of nonlinear autonomous equation with the $k$-Hessian operator. We also give some interesting qualitative properties of solutions. We provide an approach, based upon a Pohozaev-type identity, that unifies all our results.

Keywords

• uniqueness
• liouville-type theorem
• radial solutions
• $k$-hessian operators