Multiple Solutions for Double Phase Problems with Hardy Type Potential
In this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/4/376 |
| _version_ | 1797396735824232448 |
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| author | Chun-Bo Lian Bei-Lei Zhang Bin Ge |
| author_facet | Chun-Bo Lian Bei-Lei Zhang Bin Ge |
| author_sort | Chun-Bo Lian |
| collection | DOAJ |
| description | In this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general assumptions on the nonlinearity <i>f</i>. Here we use Ricceri’s variational principle and Bonanno’s three critical points theorem in order to overcome the lack of compactness. |
| first_indexed | 2024-03-09T00:55:53Z |
| format | Article |
| id | doaj.art-a25d32669e2c432fb2049293c0b8341c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T00:55:53Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a25d32669e2c432fb2049293c0b8341c2023-12-11T16:56:55ZengMDPI AGMathematics2227-73902021-02-019437610.3390/math9040376Multiple Solutions for Double Phase Problems with Hardy Type PotentialChun-Bo Lian0Bei-Lei Zhang1Bin Ge2College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, ChinaCollege of Mathematical Sciences, Harbin Engineering University, Harbin 150001, ChinaCollege of Mathematical Sciences, Harbin Engineering University, Harbin 150001, ChinaIn this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general assumptions on the nonlinearity <i>f</i>. Here we use Ricceri’s variational principle and Bonanno’s three critical points theorem in order to overcome the lack of compactness.https://www.mdpi.com/2227-7390/9/4/376double phase operatorsingular problemvariational methods |
| spellingShingle | Chun-Bo Lian Bei-Lei Zhang Bin Ge Multiple Solutions for Double Phase Problems with Hardy Type Potential Mathematics double phase operator singular problem variational methods |
| title | Multiple Solutions for Double Phase Problems with Hardy Type Potential |
| title_full | Multiple Solutions for Double Phase Problems with Hardy Type Potential |
| title_fullStr | Multiple Solutions for Double Phase Problems with Hardy Type Potential |
| title_full_unstemmed | Multiple Solutions for Double Phase Problems with Hardy Type Potential |
| title_short | Multiple Solutions for Double Phase Problems with Hardy Type Potential |
| title_sort | multiple solutions for double phase problems with hardy type potential |
| topic | double phase operator singular problem variational methods |
| url | https://www.mdpi.com/2227-7390/9/4/376 |
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