Sign-Changing multi-bump solutions for nonlinear schrödinger equations with steep potential wells

Yohei Sato, Kazunaga Tanaka

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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 → ∞.

Original languageEnglish
Pages (from-to)6205-6253
Number of pages49
JournalTransactions of the American Mathematical Society
Volume361
Issue number12
DOIs
Publication statusPublished - 2009 Dec 1

Keywords

  • Critical frequency
  • Nonlinear schrödinger equations
  • Sign-changing solutions
  • Singular perturbation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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