Semiclassical Solutions for a Kind of Coupled Schrödinger Equations

In this paper, we are concerned with the following coupled Schrödinger equations −λ2Δu+a1xu=cxv+a2xup−2u+a3xu2∗−2u,x∈ℝN,−λ2Δv+b1xv=cxu+b2xvp−2v+b3xv2∗−2v,x∈ℝN, where 2

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Published in:Advances in mathematical physics 2020, Vol.2020 (2020), p.1-6
Main Authors: Fan, Jinmei, Zhang, Qiongfen, Jiang, Yi-rong
Format: Article
Language:English
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Inequality
Mathematical analysis
Partial differential equations
Schrodinger equation
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description In this paper, we are concerned with the following coupled Schrödinger equations −λ2Δu+a1xu=cxv+a2xup−2u+a3xu2∗−2u,x∈ℝN,−λ2Δv+b1xv=cxu+b2xvp−2v+b3xv2∗−2v,x∈ℝN, where 2
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Under some suitable conditions that a10=infa1=0 or b10=infb1=0 and cx2≤ϑa1xb1x with ϑ∈0,1, the above coupled Schrödinger system possesses nontrivial solutions if λ∈0,λ0, where λ0 is related to a1,a2,a3,b1,b2,b3, and N.</description><identifier>ISSN: 1687-9120</identifier><identifier>EISSN: 1687-9139</identifier><identifier>DOI: 10.1155/2020/4378691</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Inequality ; Mathematical analysis ; Partial differential equations ; Schrodinger equation</subject><ispartof>Advances in mathematical physics, 2020, Vol.2020 (2020), p.1-6</ispartof><rights>Copyright © 2020 Jinmei Fan et al.</rights><rights>Copyright © 2020 Jinmei Fan et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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subjects Inequality
Mathematical analysis
Partial differential equations
Schrodinger equation
title Semiclassical Solutions for a Kind of Coupled Schrödinger Equations
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