A NECESSARY AND A SUFFICIENT CONDITION FOR THE EXISTENCE OF THE POSITIVE RADIAL SOLUTIONS TO HESSIAN EQUATIONS AND SYSTEMS WITH WEIGHTS

doi:10.1016/S0252-9602(16)30114-X

Abstract

Abstract:

In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou (existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters, Volume 50, December 2015, Pages 48-55).

Key words: existence, Keller-Osserman condition, k-Hessian equation and system

Dragos-Patru COVEI. A NECESSARY AND A SUFFICIENT CONDITION FOR THE EXISTENCE OF THE POSITIVE RADIAL SOLUTIONS TO HESSIAN EQUATIONS AND SYSTEMS WITH WEIGHTS[J].Acta mathematica scientia,Series B, 2017, 37(1): 47-57.

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