On variational nonlinear equations with monotone operators
Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations. We investigate when functional whose minimum is obtained by a direct method of the calculus of varia...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-08-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2020-0102 |
| _version_ | 1818581848821858304 |
|---|---|
| author | Galewski Marek |
| author_facet | Galewski Marek |
| author_sort | Galewski Marek |
| collection | DOAJ |
| description | Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations. We investigate when functional whose minimum is obtained by a direct method of the calculus of variations satisfies the Palais-Smale condition, relate minimizing sequence and Galerkin approximaitons when both exist, then provide structure conditions on the derivative of the action functional under which bounded Palais-Smale sequences are convergent. Finally, we make some comment concerning the convergence of Palais-Smale sequence obtained in the mountain pass theorem due to Rabier. |
| first_indexed | 2024-12-16T07:40:01Z |
| format | Article |
| id | doaj.art-ce275b5927044cd087478445300012ed |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-12-16T07:40:01Z |
| publishDate | 2020-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-ce275b5927044cd087478445300012ed2022-12-21T22:39:07ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2020-08-0110128930010.1515/anona-2020-0102anona-2020-0102On variational nonlinear equations with monotone operatorsGalewski Marek0Institute of Mathematics, Lodz University of Technology, Wolczanska, 215, 90-924, Lodz, PolandUsing monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations. We investigate when functional whose minimum is obtained by a direct method of the calculus of variations satisfies the Palais-Smale condition, relate minimizing sequence and Galerkin approximaitons when both exist, then provide structure conditions on the derivative of the action functional under which bounded Palais-Smale sequences are convergent. Finally, we make some comment concerning the convergence of Palais-Smale sequence obtained in the mountain pass theorem due to Rabier.https://doi.org/10.1515/anona-2020-0102monotone operatordirect variational methodpalais-smale conditionminimizing sequence49j4047j0547j30 |
| spellingShingle | Galewski Marek On variational nonlinear equations with monotone operators Advances in Nonlinear Analysis monotone operator direct variational method palais-smale condition minimizing sequence 49j40 47j05 47j30 |
| title | On variational nonlinear equations with monotone operators |
| title_full | On variational nonlinear equations with monotone operators |
| title_fullStr | On variational nonlinear equations with monotone operators |
| title_full_unstemmed | On variational nonlinear equations with monotone operators |
| title_short | On variational nonlinear equations with monotone operators |
| title_sort | on variational nonlinear equations with monotone operators |
| topic | monotone operator direct variational method palais-smale condition minimizing sequence 49j40 47j05 47j30 |
| url | https://doi.org/10.1515/anona-2020-0102 |
| work_keys_str_mv | AT galewskimarek onvariationalnonlinearequationswithmonotoneoperators |