Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy terms
In order to study a class of quasilinear p-biharmonic equations with Hardy terms and multi-critical Sobolev-Hardy exponents, the existence theorem of the solutions to the above problem is established by means of the Ekeland variational principle. Firstly, to guarantee the variational functional is b...
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Hebei University of Science and Technology
2019-04-01
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| Series: | Journal of Hebei University of Science and Technology |
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| Online Access: | http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201902004&flag=1&journal_ |
| _version_ | 1828866857165127680 |
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| author | Yan REN Yanbin SANG |
| author_facet | Yan REN Yanbin SANG |
| author_sort | Yan REN |
| collection | DOAJ |
| description | In order to study a class of quasilinear p-biharmonic equations with Hardy terms and multi-critical Sobolev-Hardy exponents, the existence theorem of the solutions to the above problem is established by means of the Ekeland variational principle. Firstly, to guarantee the variational functional is bounded from below, it is restricted on a set Mη (usually called Nehari manifold). Secondly, the set Mη is divided into three parts M+η, M0η and M-η by using fibering maps. Moreover, the existence of minimum in M+η and M-η is proved by studying the properties of the two subsets. Finally, by using implicit function theorem, it is found that there exists a minimizing sequence {un} making the (PS)c conditions hold when the parameters satisfy certain conditions. Therefore, the existence of the solutions to the problem is proved. The conclusions provide a theoretical basis for judging the structure and properties of the solutions. |
| first_indexed | 2024-12-13T04:59:49Z |
| format | Article |
| id | doaj.art-fdda4def33c14794a0db8058d4985a01 |
| institution | Directory Open Access Journal |
| issn | 1008-1542 |
| language | zho |
| last_indexed | 2024-12-13T04:59:49Z |
| publishDate | 2019-04-01 |
| publisher | Hebei University of Science and Technology |
| record_format | Article |
| series | Journal of Hebei University of Science and Technology |
| spelling | doaj.art-fdda4def33c14794a0db8058d4985a012022-12-21T23:58:49ZzhoHebei University of Science and TechnologyJournal of Hebei University of Science and Technology1008-15422019-04-0140211912410.7535/hbkd.2019yx02004b201902004Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy termsYan REN0Yanbin SANG1School of Science, North University of China, Taiyuan, Shanxi 030051, ChinaSchool of Science, North University of China, Taiyuan, Shanxi 030051, ChinaIn order to study a class of quasilinear p-biharmonic equations with Hardy terms and multi-critical Sobolev-Hardy exponents, the existence theorem of the solutions to the above problem is established by means of the Ekeland variational principle. Firstly, to guarantee the variational functional is bounded from below, it is restricted on a set Mη (usually called Nehari manifold). Secondly, the set Mη is divided into three parts M+η, M0η and M-η by using fibering maps. Moreover, the existence of minimum in M+η and M-η is proved by studying the properties of the two subsets. Finally, by using implicit function theorem, it is found that there exists a minimizing sequence {un} making the (PS)c conditions hold when the parameters satisfy certain conditions. Therefore, the existence of the solutions to the problem is proved. The conclusions provide a theoretical basis for judging the structure and properties of the solutions.http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201902004&flag=1&journal_nonlinear functional analysiscritical Sobolev-Hardy termsquasilinear p-biharmonic equationsEkeland's variational principleexistence of the solution |
| spellingShingle | Yan REN Yanbin SANG Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy terms Journal of Hebei University of Science and Technology nonlinear functional analysis critical Sobolev-Hardy terms quasilinear p-biharmonic equations Ekeland's variational principle existence of the solution |
| title | Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy terms |
| title_full | Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy terms |
| title_fullStr | Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy terms |
| title_full_unstemmed | Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy terms |
| title_short | Existence of solutions for quasilinear p-biharmonic equations with critical Sobolev-Hardy terms |
| title_sort | existence of solutions for quasilinear p biharmonic equations with critical sobolev hardy terms |
| topic | nonlinear functional analysis critical Sobolev-Hardy terms quasilinear p-biharmonic equations Ekeland's variational principle existence of the solution |
| url | http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201902004&flag=1&journal_ |
| work_keys_str_mv | AT yanren existenceofsolutionsforquasilinearpbiharmonicequationswithcriticalsobolevhardyterms AT yanbinsang existenceofsolutionsforquasilinearpbiharmonicequationswithcriticalsobolevhardyterms |