Existence for a k-Hessian equation involving supercritical growth

Abstract In this paper we use variational techniques to give existence results for the problem { S k [ u ] = f ( x , − u ) in Ω u 0 in Ω u = 0 on ∂ 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 Poincare (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.

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