Existence for a K-Hessian Equation Involving Supercritical Growth

In this paper we use variational techniques to give existence results for the problem {S k [u]=f(x,−u)inΩu<0inΩu=0on∂Ω where S k [u] is the k-Hessian operator and f(x,u) is a supercritical nonlinearity in the sense introduced by [K. Tso, Ann. Inst. Henri Poincaré (1990)]. Using some ideas from a celebrated article by Brezis and Nirenberg we show existence of a positive solution considering supercritical nonlinearities, which is surprising given the validity of the Pohozaev identity. © 2019 Elsevier Inc.