Existence of Solutions for a Modified Nonlinear Schrödinger System

We are concerned with the following modified nonlinear Schrödinger system: -Δu+u-(1/2)uΔ(u2)=(2α/(α+β))|u|α-2|v|βu,  x∈Ω,  -Δv+v-(1/2)vΔ(v2)=(2β/(α+β))|u|α|v|β-2v,  x∈Ω,  u=0,  v=0,  x∈∂Ω, where α>2,  β>2,  α+β<2·2*,  2*=2N/(N-2) is the critical...

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Main Authors: Yujuan Jiao, Yanli Wang
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/431672
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author Yujuan Jiao
Yanli Wang
author_facet Yujuan Jiao
Yanli Wang
author_sort Yujuan Jiao
collection DOAJ
description We are concerned with the following modified nonlinear Schrödinger system: -Δu+u-(1/2)uΔ(u2)=(2α/(α+β))|u|α-2|v|βu,  x∈Ω,  -Δv+v-(1/2)vΔ(v2)=(2β/(α+β))|u|α|v|β-2v,  x∈Ω,  u=0,  v=0,  x∈∂Ω, where α>2,  β>2,  α+β<2·2*,  2*=2N/(N-2) is the critical Sobolev exponent, and Ω⊂ℝN  (N≥3) is a bounded smooth domain. By using the perturbation method, we establish the existence of both positive and negative solutions for this system.
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institution Kabale University
issn 1110-757X
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language English
publishDate 2013-01-01
publisher Wiley
record_format Article
series Journal of Applied Mathematics
spelling doaj-art-34097ec5c5f643c9b6124f7216cf4f932025-08-20T03:55:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/431672431672Existence of Solutions for a Modified Nonlinear Schrödinger SystemYujuan Jiao0Yanli Wang1College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, ChinaSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, ChinaWe are concerned with the following modified nonlinear Schrödinger system: -Δu+u-(1/2)uΔ(u2)=(2α/(α+β))|u|α-2|v|βu,  x∈Ω,  -Δv+v-(1/2)vΔ(v2)=(2β/(α+β))|u|α|v|β-2v,  x∈Ω,  u=0,  v=0,  x∈∂Ω, where α>2,  β>2,  α+β<2·2*,  2*=2N/(N-2) is the critical Sobolev exponent, and Ω⊂ℝN  (N≥3) is a bounded smooth domain. By using the perturbation method, we establish the existence of both positive and negative solutions for this system.http://dx.doi.org/10.1155/2013/431672
spellingShingle Yujuan Jiao
Yanli Wang
Existence of Solutions for a Modified Nonlinear Schrödinger System
Journal of Applied Mathematics
title Existence of Solutions for a Modified Nonlinear Schrödinger System
title_full Existence of Solutions for a Modified Nonlinear Schrödinger System
title_fullStr Existence of Solutions for a Modified Nonlinear Schrödinger System
title_full_unstemmed Existence of Solutions for a Modified Nonlinear Schrödinger System
title_short Existence of Solutions for a Modified Nonlinear Schrödinger System
title_sort existence of solutions for a modified nonlinear schrodinger system
url http://dx.doi.org/10.1155/2013/431672
work_keys_str_mv AT yujuanjiao existenceofsolutionsforamodifiednonlinearschrodingersystem
AT yanliwang existenceofsolutionsforamodifiednonlinearschrodingersystem