Semiclassical standing waves with clustering peaks for nonlinear Schrödinger equations
著者
書誌事項
Semiclassical standing waves with clustering peaks for nonlinear Schrödinger equations
（Memoirs of the American Mathematical Society, v. 229,
American Mathematical Society, 2014
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注記
"Volume 229, Number 1076 (third of 5 numbers), May 2014"
Bibliography: p. 87-89
内容説明・目次
内容説明
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 .
目次
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
「Nielsen BookData」 より
