On the number of positive solutions of singularly perturbed ID nonlinear Schrödinger equations

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

研究成果: Article査読

5 被引用数 (Scopus)

抄録

We study singularly perturbed ID nonlinear Schrödinger equations (1.1). When V(x) has multiple critical points, (1.1) has a wide variety of positive solutions for small ε and the number of positive solutions increases to ∞ as ε → 0. We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of V(x). Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.

本文言語English
ページ(範囲)253-268
ページ数16
ジャーナルJournal of the European Mathematical Society
8
2
DOI
出版ステータスPublished - 2006

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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