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In this paper we study solutions, possibly unbounded and sign-changing, of a weighted static Choquard equation involving the Grushin operator. Under some appropriate assumptions on the parameters, we prove various Liouville-type theorems for weak solutions under the assumption that they are stable or stable outside a compact set of Rn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\mathbb{R}^{n}$\end{document}. First, we establish the standard integral estimates via stability property to derive the nonexistence results for stable weak solutions. Next, by means of the Pohozaev identity, we deduce the Liouville-type theorem for weak solutions which are stable outside a compact set.
Acta Applicandae Mathematicae – Springer Journals
Published: Jun 1, 2023
Keywords: Choquard equation; Weighted equation; Liouville-type theorems; Grushin operator; Stable solutions; Stability outside a compact set; Pohozaev identity
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