TY - JOUR
T1 - Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations
AU - Byeon, Jaeyoung
AU - Kwon, Ohsang
AU - Oshita, Yoshihito
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/5/1
Y1 - 2015/5/1
N2 - For k = 1, · · ·, K, let Mk be a qk-dimensional smooth compact framed manifold in ℝN with qk ∈ {1, · · ·, N - 1}. We consider the equation -ε2Δu + V(x)u - up = 0 in ℝN where for each k ∈ {1, · · ·, K} and some mk > 0, V(x) = |dist(x, Mk)|mk + O(|dist(x, Mk)|mk+1) as dist(x, Mk) → 0. For a sequence of ε converging to zero, we will find a positive solution uε of the equation which concentrates on M1 ∪ · · · ∪ MK.
AB - For k = 1, · · ·, K, let Mk be a qk-dimensional smooth compact framed manifold in ℝN with qk ∈ {1, · · ·, N - 1}. We consider the equation -ε2Δu + V(x)u - up = 0 in ℝN where for each k ∈ {1, · · ·, K} and some mk > 0, V(x) = |dist(x, Mk)|mk + O(|dist(x, Mk)|mk+1) as dist(x, Mk) → 0. For a sequence of ε converging to zero, we will find a positive solution uε of the equation which concentrates on M1 ∪ · · · ∪ MK.
KW - Concentration phenomena
KW - Infinite dimensional reduction
KW - Nondegeneracy
KW - Nonlinear schrdinger equation
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U2 - 10.3934/cpaa.2015.14.825
DO - 10.3934/cpaa.2015.14.825
M3 - Article
AN - SCOPUS:84923972774
VL - 14
SP - 825
EP - 842
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
SN - 1534-0392
IS - 3
ER -