Semiclassical Standing Waves with Clustering Peaks for Nonlinear Schrodinger Equations
Author:   Jaeyoung Byeon ,  Kazunaga Tanaka
Publisher:   American Mathematical Society
ISBN:  

9780821891636


Pages:   89
Publication Date:   30 April 2014
Format:   Paperback
Availability:   In Print   Availability explained
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Semiclassical Standing Waves with Clustering Peaks for Nonlinear Schrodinger Equations


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Overview

The authors study the following singularly perturbed problem: −ϵ 2 Δu V(x)u=f(u) in R N . Their main result is the existence of a family of solutions with peaks that cluster near a local maximum of V(x) . A local variational and deformation argument in an infinite dimensional space is developed to establish the existence of such a family for a general class of nonlinearities f .

Full Product Details

Author:   Jaeyoung Byeon ,  Kazunaga Tanaka
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.164kg
ISBN:  

9780821891636


ISBN 10:   0821891634
Pages:   89
Publication Date:   30 April 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Introduction and results Preliminaries Local centers of mass Neighborhood Ω ϵ (ρ,R,ß) and minimization for a tail of u in Ω ϵ A gradient estimate for the energy functional Translation flow associated to a gradient flow of V(x) on R N Iteration procedure for the gradient flow and the translation flow An (N 1)ℓ 0 -dimensional initial path and an intersection result Completion of the proof of Theorem 1.3 Proof of Proposition 8.3 Proof of Lemma 6.1 Generalization to a saddle point setting Bibliography

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Author Information

Jaeyoung Byeon, KAIST, Daejeon, Republic of Korea. Kazunaga Tanaka, Waseda University, Tokyo, Japan.

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