TY - JOUR
T1 - Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations
AU - Byeon, Jaeyoung
AU - Oshita, Yoshihito
N1 - Funding Information:
The research of the first author was supported in part by KRF-2002-070-C000005 of Korea Research Foundation.
PY - 2004
Y1 - 2004
N2 - For elliptic equations of the form ε2Δu - V(x)u + up = 0, x ∈ RN, where the potential V satisfies lim inf |x|→∞ V(x) > infRN V(x) = 0, we prove the existence of new kinds of solutions, corresponding to semi-classical standing waves for nonlinear Schrödinger equations, with several local maximum points whose local maximum values are of different scales with respect to ε → 0.
AB - For elliptic equations of the form ε2Δu - V(x)u + up = 0, x ∈ RN, where the potential V satisfies lim inf |x|→∞ V(x) > infRN V(x) = 0, we prove the existence of new kinds of solutions, corresponding to semi-classical standing waves for nonlinear Schrödinger equations, with several local maximum points whose local maximum values are of different scales with respect to ε → 0.
KW - Critical frequency
KW - Nondegeneracy
KW - Nonlinear Schrodinger equations
KW - Standing waves
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U2 - 10.1081/PDE-200040205
DO - 10.1081/PDE-200040205
M3 - Article
AN - SCOPUS:10844253774
VL - 29
SP - 1877
EP - 1904
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 11-12
ER -