Abstract
We study the nonlinear Schrodinger equations: (P λ ) ―Δu+(λ 2 a(x)+1)u = |u| p―1 u, u ∈ H 1 (R N ), 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 Ω 1 and Ω 2 . We study the existence of solutions (u λ ) of (P λ ) which converge to 0 in R N (Ω 1 U Ω 2 ) and to a prescribed pair (v 1 (x), v 2 (x)) of solutions of the limit problem: ―Δv i + v i = |v i | P―1 v i in Ω i (i = 1, 2) as λ → oo.
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