J. P. A. Apaza

Asymptotic Behavior of Radial Solutions to Singular $p$-Laplacian Equations as $p\to1$

We study the singular limit $p \downarrow 1$ for positive radial entire solutions $u_p$ of $$ -\Delta_p u_p=F_p\left(|x|, u_p,\left|\nabla u_p\right|\right) u_p^{-\beta_p} \quad \text { in } \mathbb{R}^n, $$ where $n \geq 2,1<p<\min \{2, \sqrt{n}\}$, and $0 \leq \beta_p \leq p-1$. Assuming that $$ F_p \rightarrow F_1 \...