Asymptotic non-degeneracy of multiple blowup solutions to the Liouville–Gel’fand problem with an inhomogeneous coefficient
Asymptotic non-degeneracy of multiple blowup solutions to the Liouville–Gel’fand problem with an inhomogeneous coefficient
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DOI：
10.1016/j.jmaa.2012.09.028
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发表时间：
2013-02
影响因子：
1.3
通讯作者：
H. Ohtsuka;Tomohiko Sato;Takashi Suzuki
中科院分区：
文献类型：
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作者：
H. Ohtsuka;Tomohiko Sato;Takashi Suzuki
研究了二维有界光滑区域上具有Dirichlet边界条件的Liouville-Gel'fand问题−Δu=λ Veuu的多点爆破解的渐近非退化性.这里λ>0是一个参数，V是Ω上的一个正C1函数。已知解集中于哈密顿量的临界点λ↓0。我们证明，如果这个临界点是非退化的，那么相关的解决方案是线性非退化的，这是一个自然的情况V 1的延伸。在证明中使用技术修改来控制剩余项。
We study asymptotic non-degeneracy of multi-point blowup solutions to the Liouville–Gel’fand problem −Δu=λVeuin a two-dimensional bounded smooth domain with a Dirichlet boundary condition. Here λ>0 is a parameter and V is a positive C1function on Ω̄. It is known that the solution concentrates on a critical point of a Hamiltonian as λ↓0. We show that if this critical point is non-degenerate, then the associated solution is linearly non-degenerate, which is a natural extension of the case V≡1. Technical modifications are used in the proof to control residual terms.