The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation
| Autor: | Minbo Yang, Fashun Gao |
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| Rok vydání: | 2018 |
| Předmět: |
Mathematics::Functional Analysis
General Mathematics 010102 general mathematics Mathematics::Analysis of PDEs Boundary (topology) Type (model theory) Lipschitz continuity 01 natural sciences Omega Sobolev inequality 010101 applied mathematics Combinatorics Bounded function Domain (ring theory) 0101 mathematics Critical exponent Mathematics |
| Zdroj: | Science China Mathematics. 61:1219-1242 |
| ISSN: | 1869-1862 1674-7283 |
| DOI: | 10.1007/s11425-016-9067-5 |
| Popis: | We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation $$ - \Delta u = \left( {\int_\Omega {\frac{{{{\left| {u\left( y \right)} \right|}^{2_\mu ^*}}}}{{{{\left| {x - y} \right|}^\mu }}}dy} } \right){\left| u \right|^{2_\mu ^* - 2}}u + \lambda uin\Omega ,$$ , where Ω is a bounded domain of R N with Lipschitz boundary, λ is a real parameter, N ≥ 3, $$2_\mu ^* = \left( {2N - \mu } \right)/\left( {N - 2} \right)$$ is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality. |
| Databáze: | OpenAIRE |
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