2014 Fiscal Year Final Research Report
Concentration phenomena arising in nonlinear partial differential equations
| Project/Area Number |
23740079
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Okayama University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | 楕円形方程式 |
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| Outline of Final Research Achievements |
We consider the equation nonlinear elliptic equations on Euclidean space, and study the case that the potential vanishes on a finite number of smooth compact framed sub manifolds in a critical frequency case. When the connected components of zero sets of the potential function are compact smooth framed manifolds, we consider the positive solutions which concentrates on the zero level manifolds, and that its limiting profiles are positive radially symmetric solutions in the space of the same dimension as the codimensions of the zero level manifolds.
Using Lyapunov--Schmidt reduction method, for a sequence of ε converging to zero, we will find a positive solution of the equation .
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| Free Research Field |
非線形偏微分方程式
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