Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains
In the present paper, we study the p-Laplace equation in a hollow symmetric bounded domain. Let H and G be closed subgroups of the orthogonal group such that H⊊G{H\varsubsetneq G}. Then we prove the existence of a positive solution which is H-invariant and G-non-invariant. Furthermore, we give sever...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-04-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2017-6023 |
| _version_ | 1828741863877640192 |
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| author | Kajikiya Ryuji |
| author_facet | Kajikiya Ryuji |
| author_sort | Kajikiya Ryuji |
| collection | DOAJ |
| description | In the present paper, we study the p-Laplace equation in a hollow symmetric bounded domain. Let H and G be closed subgroups of the orthogonal group such that H⊊G{H\varsubsetneq G}. Then we prove the existence of a positive solution which is H-invariant and G-non-invariant. Furthermore, we give several examples of H, G and Ω, and find symmetric and asymmetric solutions. |
| first_indexed | 2024-04-13T01:07:26Z |
| format | Article |
| id | doaj.art-5074f037d11f476bbd967f064b6311ae |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-13T01:07:26Z |
| publishDate | 2018-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-5074f037d11f476bbd967f064b6311ae2022-12-22T03:09:16ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752018-04-0118230332110.1515/ans-2017-6023Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow DomainsKajikiya Ryuji0Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, JapanIn the present paper, we study the p-Laplace equation in a hollow symmetric bounded domain. Let H and G be closed subgroups of the orthogonal group such that H⊊G{H\varsubsetneq G}. Then we prove the existence of a positive solution which is H-invariant and G-non-invariant. Furthermore, we give several examples of H, G and Ω, and find symmetric and asymmetric solutions.https://doi.org/10.1515/ans-2017-6023group invariant solutionleast energy solutionpositive solution,variational method35j20 35j25 |
| spellingShingle | Kajikiya Ryuji Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains Advanced Nonlinear Studies group invariant solution least energy solution positive solution,variational method 35j20 35j25 |
| title | Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains |
| title_full | Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains |
| title_fullStr | Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains |
| title_full_unstemmed | Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains |
| title_short | Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains |
| title_sort | symmetric and asymmetric solutions of p laplace elliptic equations in hollow domains |
| topic | group invariant solution least energy solution positive solution,variational method 35j20 35j25 |
| url | https://doi.org/10.1515/ans-2017-6023 |
| work_keys_str_mv | AT kajikiyaryuji symmetricandasymmetricsolutionsofplaplaceellipticequationsinhollowdomains |