Multiplicity of bounded solutions to the $k$-Hessian equation with a Matukuma-type source

Abstract

The aim of this paper is to deal with the k-Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the problemwhere B denotes the unit ball in R n , n > 2k (k ∈ N), λ > 0 is an additional parameter, q > k and µ ≥ 2. In this setting, through a transformation recently introduced by two of the authors that reduces problem (1) to a non-autonomous two-dimensional generalized Lotka-Volterra system, we prove the existence and multiplicity of solutions for the above problem combining dynamical-systems tools, the intersection number between a regular and a singular solution and the super and subsolution method.