Access the full text.
Sign up today, get DeepDyve free for 14 days.
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
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.