Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1877-1904 |
| Number of pages | 28 |
| Journal | Communications in Partial Differential Equations |
| Volume | 29 |
| Issue number | 11-12 |
| DOIs | |
| Publication status | Published - 2004 |
| Externally published | Yes |
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Keywords
- Critical frequency
- Nondegeneracy
- Nonlinear Schrodinger equations
- Standing waves
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Applied Mathematics
Cite this
Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations. / Byeon, Jaeyoung; Oshita, Yoshihito.
In: Communications in Partial Differential Equations, Vol. 29, No. 11-12, 2004, p. 1877-1904.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations
AU - Byeon, Jaeyoung
AU - Oshita, Yoshihito
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
UR - http://www.scopus.com/inward/record.url?scp=10844253774&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=10844253774&partnerID=8YFLogxK
U2 - 10.1081/PDE-200040205
DO - 10.1081/PDE-200040205
M3 - Article
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 -