Existence, uniqueness, and decay results for singular $Φ$-Laplacian systems in $\mathbb{R}^N$

Laura Gambera, Umberto Guarnotta

Published 2023-02-14Version 1

Existence of solutions to a $\Phi$-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 Diaz-Saa type result is provided.