Study of Generalized Double-Phase Problem with ς -Laplacian Operator

Elhoussain Arhrrabi, Hamza El-Houari, Abdeljabbar Ghanmi and Khaled Kefi ()
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Elhoussain Arhrrabi: Laboratory of Applied Mathematics and Scientific Calculus, Sultan Moulay Slimane University, Beni Mellal 23000, Morocco
Hamza El-Houari: AMNEA Group, Department of Mathematics, Faculty of Sciences and Techniques Errachidia, University Moulay Ismail, Meknes 50050, Morocco
Abdeljabbar Ghanmi: Department of Mathematics and Statistics, Faculty of Sciences, University of Jeddah, Jeddah 21493, Saudi Arabia
Khaled Kefi: Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia

Mathematics, 2025, vol. 13, issue 5, 1-11

Abstract: In this paper, we explore a novel class of double-phase ς -Laplacian problems involving a ϕ -Hilfer fractional operator. Employing variational techniques and weighted Musielak space theory, we establish the existence of infinitely many positive solutions under suitable assumptions on the nonlinearities. Our main results are original and significantly advance the literature on problems featuring ϕ -Hilfer derivatives and the ς -Laplacian operator.

Keywords: generalized ? -Hilfer derivative; double-phase problem; weighted Musielak space; variational methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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