TY - JOUR
T1 - Standing waves for nonlinear Schrödinger equations with a general nonlinearity
T2 - One and two dimensional cases
AU - Byeon, Jaeyoung
AU - Jeanjean, Louis
AU - Tanaka, Kazunaga
N1 - Funding Information:
The first author was supported by the Korea Research Foundation Grant (KRF-2006-013-C00072). The third author was supported in part by Grant-in-Aid for Scientific Research (C)(2)(No. 17540205) of Japan Society for the Promotion of Science.
PY - 2008/6
Y1 - 2008/6
N2 - For N = 1,2, we consider singularly perturbed elliptic equations ε2Δ u - V(x) u + f(u)= 0, u(x)> 0 on RN, 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).
AB - For N = 1,2, we consider singularly perturbed elliptic equations ε2Δ u - V(x) u + f(u)= 0, u(x)> 0 on RN, 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).
KW - Berestycki-Lions conditions
KW - Nonlinear Schrödinger equations
KW - Standing waves
KW - Variational methods
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U2 - 10.1080/03605300701518174
DO - 10.1080/03605300701518174
M3 - Article
AN - SCOPUS:45849139773
SN - 0360-5302
VL - 33
SP - 1113
EP - 1136
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 6
ER -