Nehari manifold for a singular fractional problem driven by a general non-local integrodifferential operator

Rym Chammem; Abdeljabbar Ghanmi; Mahfoudh Mechergui

doi:10.3934/dcdss.2025006

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2025. Doi: 10.3934/dcdss.2025006

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Nehari manifold for a singular fractional problem driven by a general non-local integrodifferential operator

1.
Department of Mathematics, Faculty of Sciences, Tunis El Manar University, Tunis 2092, Tunisia
2.
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia

^*Corresponding author: Abdeljabbar Ghanmi
^*Corresponding author: Abdeljabbar Ghanmi

Received: September 2024

Revised: January 2025

Early access: February 2025

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Abstract

In this paper, we study the existence and the multiplicity of solutions for a fractional problem with variable exponents and singular nonlinearity. More precisely, we use the variational and the Nehari manifold methods to prove the existence of two nontrivial solutions for such a problem which involves a general integro-differential operator of nonlocal fractional type.

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Mathematics Subject Classification: Primary: 35A15, 35J35; Secondary: 35B38.

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