Existence, uniqueness, and decay results for singular \(\Phi \)-Laplacian systems in \({\mathbb {R}}^N\)

Existence of solutions to a \(\Phi \) $\mathrm{\Phi }$ -Laplacian singular system is obtained via shifting method and variational methods. A priori estimates are furnished through De Giorgi’s technique, Talenti’s rearrangement argument, and exploiting the weak Harnack inequality, while decay of solutions is obtained via comparison with radial solutions to auxiliary problems. Finally, uniqueness is investigated, and a Díaz-Saá type result is provided.