Concentration of solutions for fractional Kirchhoff equations with discontinuous reaction
type: Item
instance of: scholarly article
title: Concentration of solutions for fractional Kirchhoff equations with discontinuous reaction
zbMATH Open document ID: 1500.35130
author: Zhisu Liu
author: Vicenţiu D. Rădulescu
author: Ziqing Yuan
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2022-10-04T00:00:00Z
review text: The authors study the following fractional Kirchhoff equation with discontinuous nonlinearity \[ \begin{cases} \left(\varepsilon^{2\alpha}a+\varepsilon^{4\alpha-3}b\int\limits_{\mathbb{R}^3}\left|\left(-\Delta\right)^{\frac{\alpha}{2}}u\right|^2 \,\mathrm{d}x\right) \left(-\Delta\right)^\alpha u +V(x)u=H(u-\beta)f(u)\quad\text{in }\mathbb{R}^3,\\ u\in H^\alpha(\mathbb{R}^3), \quad u>0, \end{cases} \] where \(\varepsilon, \beta>0\) are small parameters, \(\alpha \in (\frac{3}{4},1)\), \(a,b\) are positive constants and the function \(f\) is superlinear with subcritical growth. Based on minimax theorems, existence and concentration properties of positive solutions are shown to the problem above.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 7595887
zbMATH Keywords: fractional Kirchhoff equation
zbMATH Keywords: discontinuous nonlinearity
zbMATH Keywords: existence
zbMATH Keywords: concentration
zbMATH Keywords: variational methods
MaRDI profile type: Publication
full work available at URL: s00033-022-01849-y
OpenAlex ID: W4296193612
Wikidata QID: Q114231764
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DOI: 10.1007/S00033-022-01849-Y
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