Semiclassical standing waves with clustering peaks for nonlinear Schrödinger equations
Author(s)
Bibliographic Information
Semiclassical standing waves with clustering peaks for nonlinear Schrödinger equations
(Memoirs of the American Mathematical Society, v. 229,
American Mathematical Society, 2014
Available at 12 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"Volume 229, Number 1076 (third of 5 numbers), May 2014"
Bibliography: p. 87-89
Description and Table of Contents
Description
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 .
Table of Contents
Introduction and results
Preliminaries
Local centers of mass
Neighborhood Ω ϵ (ρ,R,β) 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
by "Nielsen BookData"