On the Hénon-type Elliptic Systems Driven by the (p,1)-Laplacian Operator: Symmetry Breaking

In recent years, significant attention has been focused on issues related to the 1 -Laplacian operator, Δ 1 . Motivated by these advancements and driven by the exploration of ( p , q ) -Laplacian systems, we delve into the phenomenon of symmetry breaking in a Hénon-type ( p , 1 ) -Laplacian system. Our primary finding establishes the existence of non-negative and non-radial solutions under specific parameter conditions. Initially, we examine the associated problem concerning the ( p , q ) -Laplacian system, which is of independent interest. This is followed by an analysis of the sequence of solutions as q approaches 1 + asymptotically.