Research article

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

  • 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.

    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

    Related Papers:

  • 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.



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