Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potential
Abstract In this paper, we study the existence of weak solutions for a nonlinear elliptic Navier boundary value problem involving the γ ( τ ) $\gamma (\tau ) $ -type triharmonic operator and Hardy potential. The main objective of this study is to establish the existence of entropy solutions for this...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02063-1 |
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| author | Abdelaziz Sabiry Salah Boulaaras Ali El Mfadel Rafik Guefaifia |
| author_facet | Abdelaziz Sabiry Salah Boulaaras Ali El Mfadel Rafik Guefaifia |
| author_sort | Abdelaziz Sabiry |
| collection | DOAJ |
| description | Abstract In this paper, we study the existence of weak solutions for a nonlinear elliptic Navier boundary value problem involving the γ ( τ ) $\gamma (\tau ) $ -type triharmonic operator and Hardy potential. The main objective of this study is to establish the existence of entropy solutions for this problem under well-structured assumptions. Our approach relies on a novel analytical framework incorporating regularization techniques to handle the non-coercive nature of the γ ( τ ) $\gamma (\tau ) $ -triharmonic operator in Sobolev spaces with variable exponent growth conditions. Additionally, we address the singularities arising from nonlinear source terms. |
| format | Article |
| id | doaj-art-ffd1c168d23945bf83ec4e30ec7d5fe1 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-ffd1c168d23945bf83ec4e30ec7d5fe12025-08-20T03:42:52ZengSpringerOpenBoundary Value Problems1687-27702025-07-012025112310.1186/s13661-025-02063-1Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potentialAbdelaziz Sabiry0Salah Boulaaras1Ali El Mfadel2Rafik Guefaifia3Laboratory LMACS, Sultan Moulay slimane UniversityDepartment of Mathematics, College of Science, Qassim UniversityLaboratory LMACS, Sultan Moulay slimane UniversityDepartment of Mathematics, College of Science, Qassim UniversityAbstract In this paper, we study the existence of weak solutions for a nonlinear elliptic Navier boundary value problem involving the γ ( τ ) $\gamma (\tau ) $ -type triharmonic operator and Hardy potential. The main objective of this study is to establish the existence of entropy solutions for this problem under well-structured assumptions. Our approach relies on a novel analytical framework incorporating regularization techniques to handle the non-coercive nature of the γ ( τ ) $\gamma (\tau ) $ -triharmonic operator in Sobolev spaces with variable exponent growth conditions. Additionally, we address the singularities arising from nonlinear source terms.https://doi.org/10.1186/s13661-025-02063-1Elliptic equationsEntropy solutionsLaplacian-like operatorsNonlinear equationsΨ-Hilfer generalized fractional |
| spellingShingle | Abdelaziz Sabiry Salah Boulaaras Ali El Mfadel Rafik Guefaifia Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potential Boundary Value Problems Elliptic equations Entropy solutions Laplacian-like operators Nonlinear equations Ψ-Hilfer generalized fractional |
| title | Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potential |
| title_full | Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potential |
| title_fullStr | Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potential |
| title_full_unstemmed | Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potential |
| title_short | Existence results for γ ( τ ) $\gamma (\tau )$ -triharmonic equation involving Navier boundary conditions and Hardy potential |
| title_sort | existence results for γ τ gamma tau triharmonic equation involving navier boundary conditions and hardy potential |
| topic | Elliptic equations Entropy solutions Laplacian-like operators Nonlinear equations Ψ-Hilfer generalized fractional |
| url | https://doi.org/10.1186/s13661-025-02063-1 |
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