Description

• Title:
  The structure of positive solutions for a Schrödinger system
• Creator:
  Dai, Guowei;
  Sun, Yimin;
  Wang, Zhi-Qiang;
  Zhang, Zhitao
• Opis:
  Using bifurcation analysis we investigate the structure of the set of positive solutions for the coupled nonlinear Schrödinger system \begin{equation*} \begin{cases} -\Delta u_1+ u_1= u_1^3+\beta u_1u_2^2 & \text{in } \mathbb{R}^N,\\ -\Delta u_2+\lambda u_2=\mu u_2^3+\beta u_2u_1^2 &\text{in } \mathbb{R}^N,\\ u_1(x),u_2(x)\rightarrow 0 &\text{as } \vert x\vert\rightarrow+\infty, \end{cases} \end{equation*} where $N=1,2,3$, $\mu$ is a positive constant, $\lambda$ and $\beta$ are positive real parameters. We prove the existence of two two-dimensional continua $\mathcal{S}_1$ and $\mathcal{S}_2$ emanating from the two sets of semi-positive solutions which cover some regions in term of $(\beta,\lambda)\in \mathbb{R}_+^2$. To do this, we establish a multi-parameter unilateral global bifurcation theorem.
• Dostępność obiektu:
  free access
• Prawa:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Data:
  2020.03.04
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  English
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 55, No 1 (March 2020); 343 - 367;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.098/25010 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.098/25011
• Temat i słowa kluczowe:
  Schrödinger systems;
  global bifurcation;
  multi-parameter;
  positive solutions;
  Primary;
  47J15;
  35Q55;
  35B32;
  35P15
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.098
• Dostawca danych:
  Akademicka Platforma Czasopism
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