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Multiple Solutions for Double-Phase Elliptic Problem with NonLocal Interaction

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Publicado en:Mathematics vol. 13, no. 8 (2025), p. 1281
Autor principal: Kefi Khaled
Otros Autores: Al-Shomrani, Mohammed M
Publicado:
MDPI AG
Materias:
Phase transitions
Differential equations
Operators (mathematics)
Critical point
Dirichlet problem
Variational methods
Boundary value problems
Acceso en línea:Citation/Abstract
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Resumen: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.
ISSN:2227-7390
DOI:10.3390/math13081281
Fuente:Engineering Database