Critical Schrödinger equations with Stein-Weiss convolution parts in \(\mathbb{R}^2\)
type: Item
instance of: scholarly article
title: Critical Schrödinger equations with Stein-Weiss convolution parts in \(\mathbb{R}^2\)
author: Liejun Shen
author: Claudianor O. Alves
published in: Journal of Differential Equations
publication date: 2022-11-28T00:00:00Z
review text: In this paper the authors study the equation \[ -\Delta u + u =\frac{1}{|x|^\beta}\left( \int_{\mathbb{R}^2} \frac{F(u)}{|x-y|^\mu|y|^\beta} \ dy\right)f(u), \ \ x\in \mathbb{R}^2, \] where \(f\) is a function with critical exponential growth, and \(F\) is a primitive. Using a general version of the Pohožaev identity, the authors employ a general minimax principle to investigate the existence of mountain-pass type solutions for the equation. Even without a monotonicity restriction on the nonlinearity \(f\), it is shown that the mountain-pass value equals the least energy level.
reviewed by: Florin Catrina
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 7623988
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Stein-Weiss convolution
zbMATH Keywords: Trudinger-Moser inequality
zbMATH Keywords: Pohožaev identity
MaRDI profile type: Publication
full work available at URL: j.jde.2022.11.005
OpenAlex ID: W4309683876
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DOI: 10.1016/J.JDE.2022.11.005
description: scientific article; zbMATH DE number 7623988