Multiple Solutions for Double-Phase Elliptic Problem with NonLocal Interaction

Khaled Kefi () and Mohammed M. Al-Shomrani ()
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Khaled Kefi: Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia
Mohammed M. Al-Shomrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2025, vol. 13, issue 8, 1-12

Abstract: This study explores the existence and multiplicity of weak solutions for a double-phase elliptic problem with nonlocal interactions, formulated as a Dirichlet boundary value problem. The associated differential operator exhibits two distinct phases governed by exponents p and q , which satisfy a prescribed structural condition. By employing critical point theory, we establish the existence of at least one weak solution and, under appropriate assumptions, demonstrate the existence of three distinct solutions. The analysis is based on abstract variational methods, with a particular focus on the critical point theorems of Bonanno and Bonanno–Marano.

Keywords: variational methods; double phase; p-Laplacian; critical point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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