Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13081281
Authors: Khaled Kefi, Mohammed M. Al-Shomrani
Institutions: Northern Border University, King Abdulaziz University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: Northern Border University
OpenAlex ID: W4409436610