Three weak solutions for double phase elliptic problem with indefinite weight.

Bibliographic Details
Title:	Three weak solutions for double phase elliptic problem with indefinite weight.
Authors:	Kefi, Khaled, Al-Shomrani, Mohammed M.
Source:	Mathematical Modelling & Control; 2026, Vol. 6 Issue 1, p1-9, 9p
Subject Terms:	Critical point theory, Variational approach (Mathematics), Differential equations, Dirichlet problem, Nonlinear theories, Elliptic differential equations
Abstract:	This paper investigates the multiplicity of weak solutions for a double-phase elliptic problem with indefinite interaction, where the nonlinearity involves a potential term k (x) that may change sign and be singular within the domain. The problem is set up as a Dirichlet boundary value problem, where the differential operator has two different phases, involving two exponents p and q that meet a certain condition. Employing critical point theory, we demonstrate that at least one solution exists, and under suitable conditions, there are at least three solutions. These results come from applying abstract variational approaches, particularly the critical point theorems by Bonanno and Marano. The manuscript also presents a detailed variational framework and sets up the necessary preliminaries to support the main results. [ABSTRACT FROM AUTHOR]
	Copyright of Mathematical Modelling & Control is the property of American Institute of Mathematical Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database:	Complementary Index

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Header	DbId: edb DbLabel: Complementary Index An: 194781606 RelevancyScore: 1041 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1041.06604003906
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Items	– Name: Title Label: Title Group: Ti Data: Three weak solutions for double phase elliptic problem with indefinite weight. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kefi%2C+Khaled%22">Kefi, Khaled</searchLink><br /><searchLink fieldCode="AR" term="%22Al-Shomrani%2C+Mohammed+M%2E%22">Al-Shomrani, Mohammed M.</searchLink> – Name: TitleSource Label: Source Group: Src Data: Mathematical Modelling & Control; 2026, Vol. 6 Issue 1, p1-9, 9p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Critical+point+theory%22">Critical point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+approach+%28Mathematics%29%22">Variational approach (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Dirichlet+problem%22">Dirichlet problem</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+theories%22">Nonlinear theories</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+differential+equations%22">Elliptic differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates the multiplicity of weak solutions for a double-phase elliptic problem with indefinite interaction, where the nonlinearity involves a potential term k (x) that may change sign and be singular within the domain. The problem is set up as a Dirichlet boundary value problem, where the differential operator has two different phases, involving two exponents p and q that meet a certain condition. Employing critical point theory, we demonstrate that at least one solution exists, and under suitable conditions, there are at least three solutions. These results come from applying abstract variational approaches, particularly the critical point theorems by Bonanno and Marano. The manuscript also presents a detailed variational framework and sets up the necessary preliminaries to support the main results. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Mathematical Modelling & Control is the property of American Institute of Mathematical Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo	BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 1 Subjects: – SubjectFull: Critical point theory Type: general – SubjectFull: Variational approach (Mathematics) Type: general – SubjectFull: Differential equations Type: general – SubjectFull: Dirichlet problem Type: general – SubjectFull: Nonlinear theories Type: general – SubjectFull: Elliptic differential equations Type: general Titles: – TitleFull: Three weak solutions for double phase elliptic problem with indefinite weight. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kefi, Khaled – PersonEntity: Name: NameFull: Al-Shomrani, Mohammed M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 27678946 Numbering: – Type: volume Value: 6 – Type: issue Value: 1 Titles: – TitleFull: Mathematical Modelling & Control Type: main
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