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

Abdeljabbar Ghanmi, Abdelhakim Sahbani and Khaled Kefi ()
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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

Mathematics, 2025, vol. 13, issue 11, 1-12

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.

Keywords: non-local integrodifferential operator; singular equation; variational methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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