2012 Fiscal Year Final Research Report
Stability analysis of standing waves for nonlinear Schrodinger equations
| Project/Area Number |
23840037
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Tsuda College (2012)
Tokyo Denki University (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2012
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| Keywords | 定在波 / 安定性 / 爆発 / 散乱 / 非線形楕円型方程式 / 特異解 / 分岐 / モース指数 |
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| Research Abstract |
In the academic year of 2011, I studied two kinds of subjects. One is concerned with a singular solution to nonlinear elliptic equations with the harmonic potential. Here, we consider the pure power nonlinearity with the Sobolev supercritical exponent. Th
In the academic year of 2012, we studied the scattering problem for the nonlinear Schrodinger equations with general nonlinearities. Here, we introduced a certain functional associated with the equations and assumed the nonlinearities satisfy the value of
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