In recent years, significant attention has been focused on issues related to the -Laplacian operator, . Motivated by these advancements and driven by the exploration of -Laplacian systems, we delve into the phenomenon of symmetry breaking in a Hénon-type -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 -Laplacian system, which is of independent interest. This is followed by an analysis of the sequence of solutions as approaches asymptotically.
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