Existence results for non-coercive problems
In this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-03-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2025-0071 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849773785415155712 |
|---|---|
| author | Diblík Josef Galewski Marek Šmarda Zdenĕk |
| author_facet | Diblík Josef Galewski Marek Šmarda Zdenĕk |
| author_sort | Diblík Josef |
| collection | DOAJ |
| description | In this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by the perturbed (negative) pp-Laplacian. As a by-product of our findings, we provide a version of the Browder-Minty theorem in the potential case that does not involve the Brouwer fixed-point theorem but utilizes optimization techniques. |
| format | Article |
| id | doaj-art-9b5fc6dece1b4d06bd73151bac670ce0 |
| institution | DOAJ |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-9b5fc6dece1b4d06bd73151bac670ce02025-08-20T03:01:57ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-03-01141pp. 385510.1515/anona-2025-0071Existence results for non-coercive problemsDiblík Josef0Galewski Marek1Šmarda Zdenĕk2Department of Mathematics, Faculty of Electrical Engineering and Communication, Technická 3058/10, Brno University of Technology, 616 00 Brno, Czech RepublicInstitute of Mathematics, Lodz University of Technology, al. Politechniki 8, 93-590 Lodz, PolandDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Technická 3058/10, Brno University of Technology, 616 00 Brno, Czech RepublicIn this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by the perturbed (negative) pp-Laplacian. As a by-product of our findings, we provide a version of the Browder-Minty theorem in the potential case that does not involve the Brouwer fixed-point theorem but utilizes optimization techniques.https://doi.org/10.1515/anona-2025-0071p-laplaciannon-coercive problemminty-browder theoremdirichlet problemmultiple solutions35a1547j0547j30 |
| spellingShingle | Diblík Josef Galewski Marek Šmarda Zdenĕk Existence results for non-coercive problems Advances in Nonlinear Analysis p-laplacian non-coercive problem minty-browder theorem dirichlet problem multiple solutions 35a15 47j05 47j30 |
| title | Existence results for non-coercive problems |
| title_full | Existence results for non-coercive problems |
| title_fullStr | Existence results for non-coercive problems |
| title_full_unstemmed | Existence results for non-coercive problems |
| title_short | Existence results for non-coercive problems |
| title_sort | existence results for non coercive problems |
| topic | p-laplacian non-coercive problem minty-browder theorem dirichlet problem multiple solutions 35a15 47j05 47j30 |
| url | https://doi.org/10.1515/anona-2025-0071 |
| work_keys_str_mv | AT diblikjosef existenceresultsfornoncoerciveproblems AT galewskimarek existenceresultsfornoncoerciveproblems AT smardazdenek existenceresultsfornoncoerciveproblems |