Semiclassical symmetric Schrödinger equations: Existence of solutions concentrating simultaneously on several spheres
Semiclassical symmetric Schrödinger equations: Existence of solutions concentrating simultaneously on several spheres
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DOI：
10.1007/s00033-006-5111-x
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发表时间：
2007-09
期刊：
影响因子：
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通讯作者：
T. Bartsch;Shuangjie Peng
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文献类型：
--
作者：
T. Bartsch;Shuangjie Peng
本文研究了径向对称薛定谔方程− ε2 <$u+ V（|X|）u= W（|X|）up，u> 0，u∈ H1（RN），其中N≥ 1，ε> 0，p> 1.当ε→ 0时，证明了同时集中在k个球面上的径向对称正解的存在性.半径位于函数Γ（r）= rN− 1 [V（r）] p+ 1 p− 1− 1的非退化临界点附近
We study the radially symmetric Schrödinger equation− ε2∆ u+ V (| x|) u= W (| x|) up, u> 0, u∈ H1 (RN), with N≥ 1, ε> 0 and p> 1. As ε→ 0, we prove the existence of positive radially symmetric solutions concentrating simultaneously on k spheres. The radii are localized near non-degenerate critical points of the function Γ (r)= rN− 1 [V (r)] p+ 1 p− 1− 1