Positive solutions of quasilinear elliptic equations with Fuchsian potentials in Wolff class

Using Harnack's inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta \in \partial\Omega\cup\{\infty\}\) for the quasilinear elliptic equation $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^...

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Veröffentlicht in:arXiv.org 2022-04
Hauptverfasser: Ratan Kr Giri, Pinchover, Yehuda
Format: Artikel
Sprache:eng
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Zusammenfassung:Using Harnack's inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta \in \partial\Omega\cup\{\infty\}\) for the quasilinear elliptic equation $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{ in } \Omega,$$ where \(\Omega\) is a domain in \(\mathbb{R}^d\), \(d\geq 2\), \(1
ISSN:2331-8422