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

TL;DR

This paper establishes existence, uniqueness, and decay properties of solutions for singular $\

Contribution

It introduces new methods for analyzing singular $\

Findings

Solutions exist under certain conditions.

Solutions decay at specific rates.

Uniqueness of solutions is proven.

Abstract

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.