On a singular nonlinear Neumann problem
We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text{(iii)}\;\ 2^*(s)\lt p+1 \leq 2^*,\) where \(2^*...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2014-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol34/2/art/opuscula_math_3417.pdf |
| _version_ | 1818187016713535488 |
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| author | Jan Chabrowski |
| author_facet | Jan Chabrowski |
| author_sort | Jan Chabrowski |
| collection | DOAJ |
| description | We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text{(iii)}\;\ 2^*(s)\lt p+1 \leq 2^*,\) where \(2^*(s)=\frac{2(N-s)}{N-2},\) \(0\lt s\lt 2,\) and \(2^*=\frac{2N}{N-2}\) denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively. |
| first_indexed | 2024-12-11T23:04:20Z |
| format | Article |
| id | doaj.art-2fa09a7159d34743aed1c4b0478e3b3e |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-11T23:04:20Z |
| publishDate | 2014-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-2fa09a7159d34743aed1c4b0478e3b3e2022-12-22T00:46:59ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742014-01-01342271290http://dx.doi.org/10.7494/OpMath.2014.34.2.2713417On a singular nonlinear Neumann problemJan Chabrowski0University of Queensland, Department of Mathematics, St. Lucia 4072, Qld, AustraliaWe investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text{(iii)}\;\ 2^*(s)\lt p+1 \leq 2^*,\) where \(2^*(s)=\frac{2(N-s)}{N-2},\) \(0\lt s\lt 2,\) and \(2^*=\frac{2N}{N-2}\) denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively.http://www.opuscula.agh.edu.pl/vol34/2/art/opuscula_math_3417.pdfNeumann problemcritical Sobolev exponentHardy-Sobolev exponent Neumann problem |
| spellingShingle | Jan Chabrowski On a singular nonlinear Neumann problem Opuscula Mathematica Neumann problem critical Sobolev exponent Hardy-Sobolev exponent Neumann problem |
| title | On a singular nonlinear Neumann problem |
| title_full | On a singular nonlinear Neumann problem |
| title_fullStr | On a singular nonlinear Neumann problem |
| title_full_unstemmed | On a singular nonlinear Neumann problem |
| title_short | On a singular nonlinear Neumann problem |
| title_sort | on a singular nonlinear neumann problem |
| topic | Neumann problem critical Sobolev exponent Hardy-Sobolev exponent Neumann problem |
| url | http://www.opuscula.agh.edu.pl/vol34/2/art/opuscula_math_3417.pdf |
| work_keys_str_mv | AT janchabrowski onasingularnonlinearneumannproblem |