Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity: One and Two Dimensional Cases
Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity: One and Two Dimensional Cases
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DOI：
10.1080/03605300701518174
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发表时间：
2008-05
影响因子：
1.9
通讯作者：
Jaeyoung Byeon;L. Jeanjean;Kazunaga Tanaka
中科院分区：
文献类型：
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作者：
Jaeyoung Byeon;L. Jeanjean;Kazunaga Tanaka
对于N = 1，2，考虑RN，lim上的奇摄动椭圆型方程<$2 Δ u − V（x）u + f（u）= 0，u（x）> 0| X| →∞ u（x）= 0。对于小的ε > 0，我们证明了在我们认为几乎最优的f条件下，存在集中在V的正局部极小值的孤立分量处的局域束缚态解;当N ≥ 3时，Byeon和Jeanjean（2007）证明了这一点。
For N = 1,2, we consider singularly perturbed elliptic equations ϵ2Δ u − V(x) u + f(u)= 0, u(x)> 0 on R N , lim|x|→∞ u(x)= 0. For small ϵ > 0, we show the existence of a localized bound state solution concentrating at an isolated component of positive local minimum of V under conditions on f we believe to be almost optimal; when N ≥ 3, it was shown in Byeon and Jeanjean (2007).