The existence of least energy sign-changing solution for Kirchhoff-type problem with potential vanishing at infinity
type: Item
instance of: scholarly article
title: The existence of least energy sign-changing solution for Kirchhoff-type problem with potential vanishing at infinity
zbMATH Open document ID: 1480.35234
DOI: 10.1155/2021/6690204
author: Ting Xiao
author: Canlin Gan
author: Qiongfen Zhang
published in: Advances in Mathematical Physics
publication date: 2021-11-17T00:00:00Z
review text: Summary: In this paper, we study the Kirchhoff-type equation: \[ -\Big(a+b \int_{\mathbb{R}^3} |\nabla u|^2 d x\Big)\varDelta u+V(x)u=Q(x) f(u), \text{ in } \mathbb{R}^3, \] where \(a, b>0\), \(f\in C^1(\mathbb{R}^3, \mathbb{R})\), and \(V, Q \in C^1(\mathbb{R}^3, \mathbb{R}^+)\). \(V(x)\) and \(Q(x)\) are vanishing at infinity. With the aid of the quantitative deformation lemma and constraint variational method, we prove the existence of a sign-changing solution \(u\) to the above equation. Moreover, we obtain that the sign-changing solution \(u\) has exactly two nodal domains. Our results can be seen as an improvement of the previous literature.
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 7428599
zbMATH Keywords: Kirchhoff-type equation
zbMATH Keywords: existence
zbMATH Keywords: variational methodes
Wikidata QID: Q114069902
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6690204
OpenAlex ID: W3127276713
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description: scientific article