Vol. 270, No. 1, 2014

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Multi-bump bound state solutions for the quasilinear Schrödinger equation with critical frequency

Yuxia Guo and Zhongwei Tang

Vol. 270 (2014), No. 1, 49–77
Abstract

We study the existence of single- and multi-bump solutions of quasilinear Schrödinger equations

Δu + λV (x)u 1 2(Δ|u|2)u = |u|p2u,

the function V being a critical frequency in the sense that inf xNV (x) = 0. We show that if the zero set of V has several isolated connected components Ω1,,Ωk such that the interior of Ωi is not empty and Ωi is smooth, then for λ > 0 large, there exists, for any nonempty subset J {1,2,,k}, a standing wave solution trapped in a neighborhood of jJΩj.

Keywords
multi-bump bound states, quasilinear Schrödinger equation, Orlicz space
Mathematical Subject Classification 2010
Primary: 35Q55
Secondary: 35J65
Milestones
Received: 16 December 2012
Revised: 19 February 2013
Accepted: 27 September 2013
Published: 2 August 2014
Authors
Yuxia Guo
Department of Mathematics
Tsinghua University
Beijing, 100084
China
Zhongwei Tang
School of Mathematical Sciences
Beijing Normal University
Laboratory of Mathematics and Complex Systems
Ministry of Education
Beijing, 100875
China