GLOBAL BIFURCATIONS AND A PRIORI BOUNDS OF POSITIVE SOLUTIONS FOR COUPLED NONLINEAR SCHROEDINGER SYSTEMS

GUOWEI DAI; RUSHUN TIAN; ZHITAO ZHANG

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GLOBAL BIFURCATIONS AND A PRIORI BOUNDS OF POSITIVE SOLUTIONS FOR COUPLED NONLINEAR SCHROEDINGER SYSTEMS

机译：全球分叉和耦合非线性施罗德格系统的正解的先验界

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In this paper, we consider the following coupled elliptic system ｛-Δu + λ_(1u) = μ1u~3 + βuv~2-γv in R~N, -Δv + λ_(2v) = μ2v~3 + βvu~2-γu in R~N, u(ⅹ), v(ⅹ)→0 as ｜x｜→ +∞. Under symmetric assumptions λ_1 = λ_2, μ_1 = μ_2, we determine the number of γ-bifurcations for each β∈ 2 (-1,+∞), and study the behavior of global γ-bifurcation branches in [-1, 0]× H~1_r(R~N)×H~1_r (R~N). Moreover, several results for γ = 0, such as priori bounds, are of independent interests, which are improvements of corresponding theorems in [6] and [35].

机译：在本文中，我们考虑以下耦合椭圆系统{-ΔU+λ_（1u）=μ1u〜3 +βuv〜2-γv在r〜n，-Δv+λ_（2v）=μ2v〜3 +βvu〜2- γu在r〜n，u（ⅹ），v（ⅹ）→0as | x |→+∞。在对称假设下λ_1=λ_2，μ_1=μ_2，我们确定每个β-2（-1，+∞）的γ分叉的数量，并研究[-1,0]×中的全局γ分支分支的行为h〜1_r（r〜n）×h〜1_r（r〜n）。此外，γ= 0的几个结果，例如先验界限，具有独立的兴趣，这是[6]和[35]中的对应定理的改进。

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来源
《Discrete and continuous dynamical systems▼hSeries S》 |2019年第7期|1905-1927|共23页
作者
GUOWEI DAI; RUSHUN TIAN; ZHITAO ZHANG;
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作者单位

School of Mathematical Sciences Dalian University of Technology Dalian 116024 China;

School of Mathematical Sciences Capital Normal University Beijing 100048 China;

HLM CEMS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China;

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正文语种 eng
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关键词
Bifurcation; Schroedinger systems; positive solutions;

机译：分叉;施罗德格系统;积极的解决方案;

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2. A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system [J] . Thomas Bartsch, Norman Dancer, Zhi-Qiang Wang Calculus of Variations and Partial Differential Equations . 2010,第s3a4期

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3. POSITIVE SOLUTIONS OF DOUBLY COUPLED MULTICOMPONENT NONLINEAR SCHROEDINGER SYSTEMS [J] . JIABAO SU, RUSHUN TIAN, ZHI-QIANG WANG Discrete and continuous dynamical systems▼hSeries S . 2019,第7期

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GLOBAL BIFURCATIONS AND A PRIORI BOUNDS OF POSITIVE SOLUTIONS FOR COUPLED NONLINEAR SCHROEDINGER SYSTEMS

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