Noncoercive resonant (p,2)-equations with concave terms
We consider a nonlinear Dirichlet problem driven by the sum of a p-Laplace and a Laplacian (a (p,2){(p,2)}-equation). The reaction exhibits the competing effects of a parametric concave term plus a Caratheodory perturbation which is resonant with respect to the principle eigenvalue of the Dirichlet...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-10-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2018-0175 |
| _version_ | 1818907847984939008 |
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| author | Papageorgiou Nikolaos S. Zhang Chao |
| author_facet | Papageorgiou Nikolaos S. Zhang Chao |
| author_sort | Papageorgiou Nikolaos S. |
| collection | DOAJ |
| description | We consider a nonlinear Dirichlet problem driven by the sum of a p-Laplace and a Laplacian (a (p,2){(p,2)}-equation). The reaction exhibits the competing effects of a parametric concave term plus a Caratheodory perturbation which is resonant with respect to the principle eigenvalue of the Dirichlet p-Laplacian. Using variational methods together with truncation and comparison techniques and Morse theory (critical groups), we show that for all small values of the parameter, the problem has as least six nontrivial smooth solutions all with sign information (two positive, two negative and two nodal (sign changing)). |
| first_indexed | 2024-12-19T22:01:38Z |
| format | Article |
| id | doaj.art-2c11e66f9cad40688275bcbba32c5f89 |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-12-19T22:01:38Z |
| publishDate | 2018-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-2c11e66f9cad40688275bcbba32c5f892022-12-21T20:04:08ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2018-10-019122824910.1515/anona-2018-0175anona-2018-0175Noncoercive resonant (p,2)-equations with concave termsPapageorgiou Nikolaos S.0Zhang Chao1Department of Mathematics, National Technical University, Zografou Campus, Athens15780, GreeceDepartment of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin150001, P. R. ChinaWe consider a nonlinear Dirichlet problem driven by the sum of a p-Laplace and a Laplacian (a (p,2){(p,2)}-equation). The reaction exhibits the competing effects of a parametric concave term plus a Caratheodory perturbation which is resonant with respect to the principle eigenvalue of the Dirichlet p-Laplacian. Using variational methods together with truncation and comparison techniques and Morse theory (critical groups), we show that for all small values of the parameter, the problem has as least six nontrivial smooth solutions all with sign information (two positive, two negative and two nodal (sign changing)).https://doi.org/10.1515/anona-2018-0175concave termresonancenonlinear regularity theorynonlinear maximum principle,strong comparison principletruncationcritical groupsconstant sign and nodal solutions35j20 35j60 58e05 |
| spellingShingle | Papageorgiou Nikolaos S. Zhang Chao Noncoercive resonant (p,2)-equations with concave terms Advances in Nonlinear Analysis concave term resonance nonlinear regularity theory nonlinear maximum principle,strong comparison principle truncation critical groups constant sign and nodal solutions 35j20 35j60 58e05 |
| title | Noncoercive resonant (p,2)-equations with concave terms |
| title_full | Noncoercive resonant (p,2)-equations with concave terms |
| title_fullStr | Noncoercive resonant (p,2)-equations with concave terms |
| title_full_unstemmed | Noncoercive resonant (p,2)-equations with concave terms |
| title_short | Noncoercive resonant (p,2)-equations with concave terms |
| title_sort | noncoercive resonant p 2 equations with concave terms |
| topic | concave term resonance nonlinear regularity theory nonlinear maximum principle,strong comparison principle truncation critical groups constant sign and nodal solutions 35j20 35j60 58e05 |
| url | https://doi.org/10.1515/anona-2018-0175 |
| work_keys_str_mv | AT papageorgiounikolaoss noncoerciveresonantp2equationswithconcaveterms AT zhangchao noncoerciveresonantp2equationswithconcaveterms |