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Existence results for a singular fractional Kirchhoff problems involving the general non-local integrodifferential operator.

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Τίτλος: Existence results for a singular fractional Kirchhoff problems involving the general non-local integrodifferential operator.
Συγγραφείς: Mechergui, Mahfoudh1 (AUTHOR) mecherguimahfoud78@gmail.com
Πηγή: Mathematical Foundations of Computing. Oct2026, Vol. 13, p1-12. 12p.
Θεματικοί όροι: *Variational approach (Mathematics), *Calculus of variations, *Function spaces, *Exponents
Περίληψη: In this paper, we investigate a singular fractional Kirchhoff-type problem involving a general nonlocal integrodifferential operator with variable exponents. The considered model combines a Kirchhoff term, a singular nonlinearity, and a fractional operator of elliptic type defined through a measurable kernel satisfying suitable structural assumptions. Working within the framework of generalized fractional Sobolev spaces with variable exponents, we establish the existence of at least one nontrivial weak solution. The analysis relies on variational techniques and minimization arguments. First, the associated energy functional is shown to be coercive, bounded from below, and weakly lower semicontinuous. Then, by proving the existence of a negative energy level and applying direct methods of the calculus of variations, the existence of a global minimizer is obtained, which yields a nontrivial weak solution to the problem. An illustrative example is also provided to demonstrate the applicability of the main theorem. [ABSTRACT FROM AUTHOR]
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  Data: Existence results for a singular fractional Kirchhoff problems involving the general non-local integrodifferential operator.
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  Data: <searchLink fieldCode="AR" term="%22Mechergui%2C+Mahfoudh%22">Mechergui, Mahfoudh</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mecherguimahfoud78@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+Foundations+of+Computing%22">Mathematical Foundations of Computing</searchLink>. Oct2026, Vol. 13, p1-12. 12p.
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  Data: In this paper, we investigate a singular fractional Kirchhoff-type problem involving a general nonlocal integrodifferential operator with variable exponents. The considered model combines a Kirchhoff term, a singular nonlinearity, and a fractional operator of elliptic type defined through a measurable kernel satisfying suitable structural assumptions. Working within the framework of generalized fractional Sobolev spaces with variable exponents, we establish the existence of at least one nontrivial weak solution. The analysis relies on variational techniques and minimization arguments. First, the associated energy functional is shown to be coercive, bounded from below, and weakly lower semicontinuous. Then, by proving the existence of a negative energy level and applying direct methods of the calculus of variations, the existence of a global minimizer is obtained, which yields a nontrivial weak solution to the problem. An illustrative example is also provided to demonstrate the applicability of the main theorem. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.3934/mfc.2026023
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 1
    Subjects:
      – SubjectFull: Variational approach (Mathematics)
        Type: general
      – SubjectFull: Calculus of variations
        Type: general
      – SubjectFull: Function spaces
        Type: general
      – SubjectFull: Exponents
        Type: general
    Titles:
      – TitleFull: Existence results for a singular fractional Kirchhoff problems involving the general non-local integrodifferential operator.
        Type: main
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            NameFull: Mechergui, Mahfoudh
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          Dates:
            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
          Identifiers:
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              Value: 25778838
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            – Type: volume
              Value: 13
          Titles:
            – TitleFull: Mathematical Foundations of Computing
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