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

Xinyue Zhang; Haibo Chen; Jie Yang; Xinyue Zhang; Haibo Chen; Jie Yang

doi:10.3934/math.2025166

AIMS Mathematics

2025, Volume 10, Issue 2: 3597-3622. doi: 10.3934/math.2025166

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Research article

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

1.
School of Mathematics and Computational Science, Huaihua University, Huaihua, Hunan 418008, China
2.
School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, China
3.
Key Lab Intelligent Control Technol Wuling Mt Ecol, Huaihua 418008, Hunan, China

Received: 02 December 2024 Revised: 17 February 2025 Accepted: 18 February 2025 Published: 25 February 2025
MSC : 49J35

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.
- fractional $ p $-Laplacian,
- mass critical,
- minimizers,
- blow up
Citation: Xinyue Zhang, Haibo Chen, Jie Yang. Blow up behavior of minimizers for a fractional p-Laplace problem with external potentials and mass critical nonlinearity[J]. AIMS Mathematics, 2025, 10(2): 3597-3622. doi: 10.3934/math.2025166

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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.

References

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