Existence of solutions for Hardy-Sobolev-Maz'ya systems
The main goal of this article is to investigate the existence of solutions for the Hardy-Sobolev-Maz'ya system $$displaylines{ -Delta u-lambda frac{u}{|y|^2}=frac{|v|^{p_t-1}}{|y|^t}v,quad hbox{in }Omega,cr -Delta v-lambda frac{v}{|y|^2}=frac{|u|^{p_s-1}}{|y|^s}u,quad hbox{in }Omega,cr u...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2012-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/115/abstr.html |
| _version_ | 1831520697652871168 |
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| author | Jian Wang Xin Wei |
| author_facet | Jian Wang Xin Wei |
| author_sort | Jian Wang |
| collection | DOAJ |
| description | The main goal of this article is to investigate the existence of solutions for the Hardy-Sobolev-Maz'ya system $$displaylines{ -Delta u-lambda frac{u}{|y|^2}=frac{|v|^{p_t-1}}{|y|^t}v,quad hbox{in }Omega,cr -Delta v-lambda frac{v}{|y|^2}=frac{|u|^{p_s-1}}{|y|^s}u,quad hbox{in }Omega,cr u=v=0,quad hbox{on }partial Omega }$$ where $0inOmega$ which is a bounded, open and smooth subset of $mathbb{R}^kimes mathbb{R}^{N-k}$, $2leq k<N$. The non-existence of classical positive solutions is obtained by a variational identity and the existence result by a linking theorem. |
| first_indexed | 2024-12-13T17:36:34Z |
| format | Article |
| id | doaj.art-37de78048f7a480686942543d45acecd |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-13T17:36:34Z |
| publishDate | 2012-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-37de78048f7a480686942543d45acecd2022-12-21T23:36:53ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-07-012012115,114Existence of solutions for Hardy-Sobolev-Maz'ya systemsJian WangXin WeiThe main goal of this article is to investigate the existence of solutions for the Hardy-Sobolev-Maz'ya system $$displaylines{ -Delta u-lambda frac{u}{|y|^2}=frac{|v|^{p_t-1}}{|y|^t}v,quad hbox{in }Omega,cr -Delta v-lambda frac{v}{|y|^2}=frac{|u|^{p_s-1}}{|y|^s}u,quad hbox{in }Omega,cr u=v=0,quad hbox{on }partial Omega }$$ where $0inOmega$ which is a bounded, open and smooth subset of $mathbb{R}^kimes mathbb{R}^{N-k}$, $2leq k<N$. The non-existence of classical positive solutions is obtained by a variational identity and the existence result by a linking theorem.http://ejde.math.txstate.edu/Volumes/2012/115/abstr.htmlVariational identity(PS) conditionlinking theoremHardy-Sobolev-Maz'ya inequality |
| spellingShingle | Jian Wang Xin Wei Existence of solutions for Hardy-Sobolev-Maz'ya systems Electronic Journal of Differential Equations Variational identity (PS) condition linking theorem Hardy-Sobolev-Maz'ya inequality |
| title | Existence of solutions for Hardy-Sobolev-Maz'ya systems |
| title_full | Existence of solutions for Hardy-Sobolev-Maz'ya systems |
| title_fullStr | Existence of solutions for Hardy-Sobolev-Maz'ya systems |
| title_full_unstemmed | Existence of solutions for Hardy-Sobolev-Maz'ya systems |
| title_short | Existence of solutions for Hardy-Sobolev-Maz'ya systems |
| title_sort | existence of solutions for hardy sobolev maz ya systems |
| topic | Variational identity (PS) condition linking theorem Hardy-Sobolev-Maz'ya inequality |
| url | http://ejde.math.txstate.edu/Volumes/2012/115/abstr.html |
| work_keys_str_mv | AT jianwang existenceofsolutionsforhardysobolevmazyasystems AT xinwei existenceofsolutionsforhardysobolevmazyasystems |