The extreme solutions for a σ‐Hessian equation with a nonlinear operator

Abstract

The aim of this paper is to study the existence of extreme solutions and their properties for a general ‐Hessian equation involving a nonlinear operator. By introducing a suitable growth condition and developing a iterative technique, some new results on existence and asymptotic estimates of minimum and maximum solutions are derived. Moreover, we also establish the iterative sequences that converge uniformly to the extreme solutions.