Bounded solutions of a k-Hessian equation involving a weighted nonlinear source

Abstract

We consider the problem(1){Sk(D2u)=λ|x|σ(1−u)qin B,u<0in B,u=0on ∂B, where B denotes the unit ball in Rn, n>2k (k∈N), λ>0, q>k and σ≥0. We study the existence, multiplicity and uniqueness of radially symmetric bounded solutions of (1). The methodology for obtaining our results is based on a dynamical systems approach. For this, we introduce a new transformation which reduces problem (1) to an autonomous two-dimensional generalized Lotka–Volterra system.