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Existence of Solution for a Singular Problem with a General Non-Local Integrated Differential Operator

Author

Listed:
  • Abdeljabbar Ghanmi

    (Department of Mathematics and Statistics, College of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

  • Abdelhakim Sahbani

    (Ecole Nationale D’ingénieurs de Tunis, Laboratory of Mathematical and Numerical Modeling in Engineering Sciences, Tunis El Manar University, BP. 37, Tunis Belvédr̀e, Tunis 1002, Tunisia)

  • Khaled Kefi

    (Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia)

Abstract

This work examines a singular elliptic problem with a fractional and a non-local integrodifferential operator. The question of whether solutions exist is transformed into the existence of critical points of the associated functional energy, to be more specific. The existence of a critical point is then demonstrated by combining the variational method with some monotonicity arguments. After this, due to the singular non-linearity, we manually demonstrate that this critical point is a weak solution for such a problem.

Suggested Citation

  • Abdeljabbar Ghanmi & Abdelhakim Sahbani & Khaled Kefi, 2025. "Existence of Solution for a Singular Problem with a General Non-Local Integrated Differential Operator," Mathematics, MDPI, vol. 13(11), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1870-:d:1671156
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