A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutions
In this paper, we extend the result of Yan and Yang [16] on equations to an elliptic system involving critical Sobolev and Hardy–Sobolev exponents in bounded domains satisfying some geometric condition. In addition, we weaken the conditions on the dimension N and on the potential a(x){a(x)} set in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-02-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2015-0164 |
| _version_ | 1819290876212412416 |
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| author | Benmouloud Samira Khiddi Mustapha Sbaï Simohammed |
| author_facet | Benmouloud Samira Khiddi Mustapha Sbaï Simohammed |
| author_sort | Benmouloud Samira |
| collection | DOAJ |
| description | In this paper, we extend the result of Yan and Yang [16] on equations to an elliptic system involving critical Sobolev and Hardy–Sobolev exponents in bounded domains satisfying some geometric condition.
In addition, we weaken the conditions on the dimension N and on the potential a(x){a(x)} set in [16]. Our main result asserts, by a variational global-compactness argument, that
the condition on the dimension N can be refined from N≥7{N\geq 7} to N>max(4,⌊2s⌋+2){N>\max(4,\lfloor 2s\rfloor+2)}, where 0<s<2{0<s<2} and still end up with infinitely many solutions. |
| first_indexed | 2024-12-24T03:29:42Z |
| format | Article |
| id | doaj.art-bfc72d2c8bf54bd681d634878c98d6ea |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-12-24T03:29:42Z |
| publishDate | 2018-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-bfc72d2c8bf54bd681d634878c98d6ea2022-12-21T17:17:14ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2018-02-0171859610.1515/anona-2015-0164A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutionsBenmouloud Samira0Khiddi Mustapha1Sbaï Simohammed2E.G.A.L, Dépt. Maths, Fac. Sciences, Université Ibn Tofail, BP.133, Kénitra, MoroccoE.G.A.L, Dépt. Maths, Fac. Sciences, Université Ibn Tofail, BP.133, Kénitra, MoroccoE.G.A.L, Dépt. Maths, Fac. Sciences, Université Ibn Tofail, BP.133, Kénitra, MoroccoIn this paper, we extend the result of Yan and Yang [16] on equations to an elliptic system involving critical Sobolev and Hardy–Sobolev exponents in bounded domains satisfying some geometric condition. In addition, we weaken the conditions on the dimension N and on the potential a(x){a(x)} set in [16]. Our main result asserts, by a variational global-compactness argument, that the condition on the dimension N can be refined from N≥7{N\geq 7} to N>max(4,⌊2s⌋+2){N>\max(4,\lfloor 2s\rfloor+2)}, where 0<s<2{0<s<2} and still end up with infinitely many solutions.https://doi.org/10.1515/anona-2015-0164elliptic systeminfinitely many solutionscritical exponentvariational method35j60 35b33 |
| spellingShingle | Benmouloud Samira Khiddi Mustapha Sbaï Simohammed A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutions Advances in Nonlinear Analysis elliptic system infinitely many solutions critical exponent variational method 35j60 35b33 |
| title | A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutions |
| title_full | A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutions |
| title_fullStr | A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutions |
| title_full_unstemmed | A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutions |
| title_short | A refined bound on the dimension of ℝN for an elliptic system involving critical terms with infinitely many solutions |
| title_sort | refined bound on the dimension of rn for an elliptic system involving critical terms with infinitely many solutions |
| topic | elliptic system infinitely many solutions critical exponent variational method 35j60 35b33 |
| url | https://doi.org/10.1515/anona-2015-0164 |
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