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Master's Dissertation
DOI
10.11606/D.55.2004.tde-10122014-145721
Document
Author
Full name
Alex Eduardo Andrade Borges
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2004
Supervisor
Committee
Soares, Sérgio Henrique Monari (President)
Carvalho, Alexandre Nolasco de
Montenegro, Marcelo da Silva
Title in Portuguese
Existência e concentração de soluções para equações de Schrödinger
Keywords in Portuguese
Não disponível
Abstract in Portuguese
0 objetivo deste trabalho é estudar a existência e o comportamento de concentração de ondas estacionárias para a equação de Schrõdinger não linear ih ∂ ψ / ∂ t = h2 / 2m Δ ψ + V (x) ψ + V(x) ψ - γ ∣ p-1 ψ. Sob diferentes hipóteses em V, várias condições suficientes para a existência de soluções não triviais são estabelecidas. Em particular, quando V satisfaz uma certa condição no infinito, é provado que essas soluções se concentram em pontos de mínimo global de V quando h → 0.
Title in English
Existence and concentration of solutions for Schrödinger equations
Keywords in English
Not available
Abstract in English
The aim of this work is to studv the existence and the concentration behavior of standing wave solutions of the nonlinear Schrõdinger equation ih ∂ ψ / ∂ t = h2 / 2m Δ ψ + V (x) ψ - γ ∣ p-1 ψ. Making different assumptions on V, various sufficient conditions for the existence of nontrivial solutions are established. In particular, under certain condition on V at infinity, it is proved that these solutions concentrate at global minimum points of V as h → 0.
 
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Publishing Date
2014-12-10
 
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