Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator

Abstract

In this work, we study a class of Hénon-type equations which involve the 1-Laplacian operator in the unit ball. Under mild assumptions on the nonlinearity, the existence of radial solutions is proved and, for a parameter in a certain range, the existence of symmetry breaking is proved, through the presence of non-radial solutions. The approach is based on an approximation scheme, where a thorough analysis of the solutions of the associated p-Laplacian problems is necessary.