TY - JOUR
T1 - Sign-Changing multi-bump solutions for nonlinear schrödinger equations with steep potential wells
AU - Sato, Yohei
AU - Tanaka, Kazunaga
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2009/12
Y1 - 2009/12
N2 - We study the nonlinear Schrödinger equations: (Pλ) -Δu+(λ2a(x)+1)u = |u|p-1u, u ε H 1(RN), where p > 1 is a subcritical exponent, a(x) is a continuous function satisfying a(x) ≥ 0, 0 < lim inf |x|-∞ a(x) ≤ lim sup|x|-∞ a(x) < ∞ and a-1(0) consists of 2 connected bounded smooth components Ω1 and Ω2. We study the existence of solutions (uλ) of (Pλ) which converge to 0 in RN \ (Ω1Ω 2) and to a prescribed pair (v1(x), v2(x)) of solutions of the limit problem: -Δvi + vi = |v i|p-1vi in Ωi (i = 1, 2) as λ → ∞.
AB - We study the nonlinear Schrödinger equations: (Pλ) -Δu+(λ2a(x)+1)u = |u|p-1u, u ε H 1(RN), where p > 1 is a subcritical exponent, a(x) is a continuous function satisfying a(x) ≥ 0, 0 < lim inf |x|-∞ a(x) ≤ lim sup|x|-∞ a(x) < ∞ and a-1(0) consists of 2 connected bounded smooth components Ω1 and Ω2. We study the existence of solutions (uλ) of (Pλ) which converge to 0 in RN \ (Ω1Ω 2) and to a prescribed pair (v1(x), v2(x)) of solutions of the limit problem: -Δvi + vi = |v i|p-1vi in Ωi (i = 1, 2) as λ → ∞.
KW - Critical frequency
KW - Nonlinear schrödinger equations
KW - Sign-changing solutions
KW - Singular perturbation
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U2 - 10.1090/S0002-9947-09-04565-6
DO - 10.1090/S0002-9947-09-04565-6
M3 - Article
AN - SCOPUS:77950659711
SN - 0002-9947
VL - 361
SP - 6205
EP - 6253
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 12
ER -