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Research Article | Open Access

Blow up behavior of minimizers for a fractional p-Laplace problem with external potentials and mass critical nonlinearity

Xinyue Zhang1, Haibo Chen2, Jie Yang1,3( )
School of Mathematics and Computational Science, Huaihua University, Huaihua, Hunan 418008, China
School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, China
Key Lab Intelligent Control Technol Wuling Mt Ecol, Huaihua 418008, Hunan, China
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Abstract

In this paper, we studied the fractional p-Laplace problem with a general potential and a mass-critical nonlinearity. By using constrained variational methods, we established the existence and nonexistence of minimizers for this problem. Moreover, we investigated the blow-up behaviour of non-negative minimizers to the above equation. Finally, under a polynomial-type potential, we obtained the optimal rate of blow-up through some subtle energy estimates.

Keywords

fractional p-Laplacianmass criticalminimizersblow up
CLC number: 49J35

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 3597-3622
DOI: 10.3934/math.2025166

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Cite this article:
Zhang X, Chen H, Yang J. Blow up behavior of minimizers for a fractional p-Laplace problem with external potentials and mass critical nonlinearity. AIMS Mathematics, 2025, 10(2): 3597-3622. https://doi.org/10.3934/math.2025166

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Received: 02 December 2024
Revised: 17 February 2025
Accepted: 18 February 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)