The aim of this paper is to deal with the -Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the problem
where denotes the unit ball in , (), is an additional parameter, and . 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.
Cite this article
Yasuhito Miyamoto, Justino Sánchez, Vicente Vergara, Multiplicity of bounded solutions to the -Hessian equation with a Matukuma-type source. Rev. Mat. Iberoam. 35 (2019), no. 5, pp. 1559–1582DOI 10.4171/RMI/1092