Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials

  • Na Ba

    School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
  • Shuangjie Peng

    School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
  • Yinbin Deng

    School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China

Abstract

In this paper, we will study the existence and qualitative property of standing waves for the nonlinear Schrödinger equation , . Let and suppose that has k local minimum points. Then, for any , we prove the existence of the standing waves in having exactly l local maximum points which concentrate near l local minimum points of respectively as . The potentials and are allowed to be either compactly supported or unbounded at infinity. Therefore, we give a positive answer to a problem proposed by Ambrosetti and Malchiodi (2007) [2].

Cite this article

Na Ba, Shuangjie Peng, Yinbin Deng, Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 5, pp. 1205–1226

DOI 10.1016/J.ANIHPC.2010.05.003