Regularity and two-class conjecture for isolated singularities of p-Laplacian equations

Let $Q'(u)=0$ be the p-Laplacian type equation in a domain $\Omega$, let $\zeta\in\{0,\infty\}$ be an isolated singular point, and let $\mathcal{G}_\zeta$ denote the germs of positive solutions in punctured neighborhoods of $\zeta$. For $u,v\in\mathcal{G}_\zeta$, write $u\underset{x\to\zeta}{\sim}v$ when their ratio tends to a positive constant, and call $\zeta$ a regular point when any two such germs are comparable under the relations defined by $\sim$, $\prec$, and $\precsim$. Suppose that admits a global positive solution and that $V$ has a Fuchsian type singularity at $\zeta$. Regularity and two-class conjecture. Then: (i) $\zeta$ is a regular point of equation; (ii) equation admits a unique global positive solution of minimal growth near infinity in $\Omega\setminus\{\zeta\}$; and (iii) $\mathcal{G}_\zeta$ has exactly two equivalence classes under $\sim$. This conjecture describes the expected classification of positive solution germs near isolated singularities, including uniqueness of the minimal-growth solution and a two-class asymptotic structure. Its resolution status is not specified in the source.