Infinitely many localized semiclassical states for critical nonlinear Dirac equations
| العنوان: | Infinitely many localized semiclassical states for critical nonlinear Dirac equations |
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| المؤلفون: | Shaowei Chen, Tianxiang Gou |
| المصدر: | Nonlinearity. 34:6358-6397 |
| بيانات النشر: | IOP Publishing, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Nonlinear Dirac equation, Applied Mathematics, Dirac (video compression format), General Physics and Astronomy, Semiclassical physics, Statistical and Nonlinear Physics, Sobolev space, Compact space, Nabla symbol, Critical exponent, Mathematical Physics, Energy (signal processing), Mathematics, Mathematical physics |
| الوصف: | In this paper, we are concerned with semiclassical states to the nonlinear Dirac equation with Sobolev critical exponent − i ϵ α ⋅ ∇ u + a β u + V ( x ) u = | u | q − 2 u + | u | u in R 3 , where u : R 3 → C 4 , 2 < q < 3, ϵ > 0 is a small parameter, a > 0 is a constant, α = (α 1, α 2, α 3), α j and β are 4 × 4 Pauli-Dirac matrices. We construct an infinite sequence of semiclassical states with higher energies concentrating around the local minimum points of the potential V. The problem is strongly indefinite and the solutions correspond to critical points of the underlying energy functional at energy levels where compactness condition breaks down. The proof relies on truncation techniques, blow-up arguments together with a local type Pohozaev identity. |
| تدمد: | 1361-6544 0951-7715 |
| DOI: | 10.1088/1361-6544/ac149f |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::be5e26ee4355dfb34c24491a5d793569 https://doi.org/10.1088/1361-6544/ac149f |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi...........be5e26ee4355dfb34c24491a5d793569 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 13616544 09517715 |
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| DOI: | 10.1088/1361-6544/ac149f |