Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential

Bibliographic Details
Main Author: Chen, Jianqing
Publication Date: 2011
Other Authors: Rocha, Eugénio M.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/41619
Summary: For a class of quasilinear Schr̈odinger equations with harmonic potential of the form iΦt =-ΔΦ+|x|2Φ-|Φ|p-1Φ2(Δ |Φ|2)Φt ≥ 0, x∈RN, we prove firstly the existence of stable standing waves for 1 < p < 3 + 4/N and then study the instability of standing waves for 3 + 4 /N ≤ p < 3N+2/N-2. Our results indicate that the quasilinear term (Δ|Φ|2)Φ makes the standing waves more stable than their counterpart in the semilinear case, which is consistent with the physical phenomena and is in striking contrast with the classical semilinear Schr̈odinger equations with potential.
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spelling Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potentialVariational methodsStanding wavesStability and instabilityQuasilinear Schrödinger equationsFor a class of quasilinear Schr̈odinger equations with harmonic potential of the form iΦt =-ΔΦ+|x|2Φ-|Φ|p-1Φ2(Δ |Φ|2)Φt ≥ 0, x∈RN, we prove firstly the existence of stable standing waves for 1 < p < 3 + 4/N and then study the instability of standing waves for 3 + 4 /N ≤ p < 3N+2/N-2. Our results indicate that the quasilinear term (Δ|Φ|2)Φ makes the standing waves more stable than their counterpart in the semilinear case, which is consistent with the physical phenomena and is in striking contrast with the classical semilinear Schr̈odinger equations with potential.International Press2024-04-19T08:56:37Z2011-01-01T00:00:00Z2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/41619eng1548-159X10.4310/DPDE.2011.v8.n2.a2Chen, JianqingRocha, Eugénio M.info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:55:02Zoai:ria.ua.pt:10773/41619Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:24:08.075706Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
title Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
spellingShingle Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
Chen, Jianqing
Variational methods
Standing waves
Stability and instability
Quasilinear Schrödinger equations
title_short Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
title_full Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
title_fullStr Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
title_full_unstemmed Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
title_sort Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
author Chen, Jianqing
author_facet Chen, Jianqing
Rocha, Eugénio M.
author_role author
author2 Rocha, Eugénio M.
author2_role author
dc.contributor.author.fl_str_mv Chen, Jianqing
Rocha, Eugénio M.
dc.subject.por.fl_str_mv Variational methods
Standing waves
Stability and instability
Quasilinear Schrödinger equations
topic Variational methods
Standing waves
Stability and instability
Quasilinear Schrödinger equations
description For a class of quasilinear Schr̈odinger equations with harmonic potential of the form iΦt =-ΔΦ+|x|2Φ-|Φ|p-1Φ2(Δ |Φ|2)Φt ≥ 0, x∈RN, we prove firstly the existence of stable standing waves for 1 < p < 3 + 4/N and then study the instability of standing waves for 3 + 4 /N ≤ p < 3N+2/N-2. Our results indicate that the quasilinear term (Δ|Φ|2)Φ makes the standing waves more stable than their counterpart in the semilinear case, which is consistent with the physical phenomena and is in striking contrast with the classical semilinear Schr̈odinger equations with potential.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-01T00:00:00Z
2011
2024-04-19T08:56:37Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/41619
url http://hdl.handle.net/10773/41619
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1548-159X
10.4310/DPDE.2011.v8.n2.a2
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv International Press
publisher.none.fl_str_mv International Press
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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