TY - JOUR
T1 - On Ambrosetti-Malchiodi-Ni Conjecture for General Hypersurfaces
AU - Wang, Liping
AU - Wei, Juncheng
AU - Yang, Jun
PY - 2011/12
Y1 - 2011/12
N2 - We consider the nonlinear problem where p > 1, ε is a small parameter and V is a uniformly positive, smooth potential. Assume that R ⊂ R nis a smooth closed, stationary and non-degenerate hypersurface relative to the functional ∫ RV Σ withΣ=P+1/P-1-1/2. We prove the existence of solutions,ũ ε at least for some sequence {ε l} l which concentrate along smooth surfaces T ε close to R This result confirms the validity of the conjecture of Ambrosetti et al. in [2] for concentration of Schrödinger equation on general hypersurfaces.
AB - We consider the nonlinear problem where p > 1, ε is a small parameter and V is a uniformly positive, smooth potential. Assume that R ⊂ R nis a smooth closed, stationary and non-degenerate hypersurface relative to the functional ∫ RV Σ withΣ=P+1/P-1-1/2. We prove the existence of solutions,ũ ε at least for some sequence {ε l} l which concentrate along smooth surfaces T ε close to R This result confirms the validity of the conjecture of Ambrosetti et al. in [2] for concentration of Schrödinger equation on general hypersurfaces.
KW - Ambrosetti-Malchiodi-Ni conjecture
KW - Concentration
KW - Infinite-dimensional reduction
KW - Nonlinear Schrödinger equation
UR - https://www.scopus.com/pages/publications/84863350425
U2 - 10.1080/03605302.2011.580033
DO - 10.1080/03605302.2011.580033
M3 - 文章
AN - SCOPUS:84863350425
SN - 0360-5302
VL - 36
SP - 2117
EP - 2161
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 12
ER -