Some new existence results of positive solutions for anisotropic variable exponent operator
Abstract This work investigates positive solutions for equations involving the anisotropic variable exponent operator, a mathematical framework critical in modeling nonstandard growth phenomena. By deriving new existence results, the study advances the understanding of nonlinear partial differential...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-01999-8 |
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| _version_ | 1823861719631396864 |
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| author | Rafik Guefaifia Salah Boulaaras Rashid Jan |
| author_facet | Rafik Guefaifia Salah Boulaaras Rashid Jan |
| author_sort | Rafik Guefaifia |
| collection | DOAJ |
| description | Abstract This work investigates positive solutions for equations involving the anisotropic variable exponent operator, a mathematical framework critical in modeling nonstandard growth phenomena. By deriving new existence results, the study advances the understanding of nonlinear partial differential equations in anisotropic and variable exponent settings. These findings have significant implications for real-world applications, such as fluid dynamics, image processing, and material science, where variable growth conditions arise naturally. More specifically, the study employs methods from functional analysis to investigate the existence, nonexistence, and minimal solutions of certain anisotropic equations within the framework of generalized Sobolev spaces. |
| format | Article |
| id | doaj-art-554f7118634145849e9e7505843f7c31 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-554f7118634145849e9e7505843f7c312025-02-09T12:47:42ZengSpringerOpenBoundary Value Problems1687-27702025-02-012025111510.1186/s13661-025-01999-8Some new existence results of positive solutions for anisotropic variable exponent operatorRafik Guefaifia0Salah Boulaaras1Rashid Jan2Department of Mathematics, College of Sciences, Qassim UniversityDepartment of Mathematics, College of Sciences, Qassim UniversityInstitute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN)Abstract This work investigates positive solutions for equations involving the anisotropic variable exponent operator, a mathematical framework critical in modeling nonstandard growth phenomena. By deriving new existence results, the study advances the understanding of nonlinear partial differential equations in anisotropic and variable exponent settings. These findings have significant implications for real-world applications, such as fluid dynamics, image processing, and material science, where variable growth conditions arise naturally. More specifically, the study employs methods from functional analysis to investigate the existence, nonexistence, and minimal solutions of certain anisotropic equations within the framework of generalized Sobolev spaces.https://doi.org/10.1186/s13661-025-01999-8Anisotropic operatorSubsuper solutionsVariable exponentsExistenceVariational methodNonlinear equations |
| spellingShingle | Rafik Guefaifia Salah Boulaaras Rashid Jan Some new existence results of positive solutions for anisotropic variable exponent operator Boundary Value Problems Anisotropic operator Subsuper solutions Variable exponents Existence Variational method Nonlinear equations |
| title | Some new existence results of positive solutions for anisotropic variable exponent operator |
| title_full | Some new existence results of positive solutions for anisotropic variable exponent operator |
| title_fullStr | Some new existence results of positive solutions for anisotropic variable exponent operator |
| title_full_unstemmed | Some new existence results of positive solutions for anisotropic variable exponent operator |
| title_short | Some new existence results of positive solutions for anisotropic variable exponent operator |
| title_sort | some new existence results of positive solutions for anisotropic variable exponent operator |
| topic | Anisotropic operator Subsuper solutions Variable exponents Existence Variational method Nonlinear equations |
| url | https://doi.org/10.1186/s13661-025-01999-8 |
| work_keys_str_mv | AT rafikguefaifia somenewexistenceresultsofpositivesolutionsforanisotropicvariableexponentoperator AT salahboulaaras somenewexistenceresultsofpositivesolutionsforanisotropicvariableexponentoperator AT rashidjan somenewexistenceresultsofpositivesolutionsforanisotropicvariableexponentoperator |