A Multiplicity Theorem for Superlinear Double Phase Problems
We consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/9/1556 |
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| author | Beata Derȩgowska Leszek Gasiński Nikolaos S. Papageorgiou |
| author_facet | Beata Derȩgowska Leszek Gasiński Nikolaos S. Papageorgiou |
| author_sort | Beata Derȩgowska |
| collection | DOAJ |
| description | We consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive and by the symmetry of the behaviour at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mo>∞</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mo>∞</mo></mrow></semantics></math></inline-formula> also negative. |
| first_indexed | 2024-03-10T07:10:30Z |
| format | Article |
| id | doaj.art-501561c176cd4b2f96106ed709470954 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T07:10:30Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-501561c176cd4b2f96106ed7094709542023-11-22T15:26:34ZengMDPI AGSymmetry2073-89942021-08-01139155610.3390/sym13091556A Multiplicity Theorem for Superlinear Double Phase ProblemsBeata Derȩgowska0Leszek Gasiński1Nikolaos S. Papageorgiou2Department of Mathematics, Pedagogical University of Cracow, Podchorazych 2, 30-084 Cracow, PolandState Higher Vocational School in Tarnow, Institute of Mathematical and Natural Science, Mickiewicza 8, 33-100 Tarnow, PolandDepartment of Mathematics, National Technical University, Zografou Campus, 15780 Athens, GreeceWe consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive and by the symmetry of the behaviour at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mo>∞</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mo>∞</mo></mrow></semantics></math></inline-formula> also negative.https://www.mdpi.com/2073-8994/13/9/1556double phase operatorNehari manifoldsuperlinear reactionconstant sign and nodal solutionsMusielak–Orlicz spaces |
| spellingShingle | Beata Derȩgowska Leszek Gasiński Nikolaos S. Papageorgiou A Multiplicity Theorem for Superlinear Double Phase Problems Symmetry double phase operator Nehari manifold superlinear reaction constant sign and nodal solutions Musielak–Orlicz spaces |
| title | A Multiplicity Theorem for Superlinear Double Phase Problems |
| title_full | A Multiplicity Theorem for Superlinear Double Phase Problems |
| title_fullStr | A Multiplicity Theorem for Superlinear Double Phase Problems |
| title_full_unstemmed | A Multiplicity Theorem for Superlinear Double Phase Problems |
| title_short | A Multiplicity Theorem for Superlinear Double Phase Problems |
| title_sort | multiplicity theorem for superlinear double phase problems |
| topic | double phase operator Nehari manifold superlinear reaction constant sign and nodal solutions Musielak–Orlicz spaces |
| url | https://www.mdpi.com/2073-8994/13/9/1556 |
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