Topological Methods in Nonlinear Analysis

Multiple solitary wave solutions of nonlinear Schrödinger systems

Rushun Tian and Zhi-qiang Wang

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Abstract

Consider the $N$-coupled nonlinear elliptic system \begin{equation}\tag{${\rm P}$} \begin{cases} \displaystyle -\Delta U_j+ U_j=\mu U_j^3+\beta U_j\sum_{k\neq j} U_k^2 \quad \text{in } \Omega,\\ U_j> 0 \quad\text{in } \Omega,\quad U_j=0 \quad \text{on } \partial\Omega,\ j=1, \ldots, N. \end{cases} \end{equation} where $\Omega$ is a smooth and bounded (or unbounded if $\Omega$ is radially symmetric) domain in $\mathbb R^n$, $n\leq3$. By using a $Z_N$ index theory, we prove the existence of multiple solutions of (P) and show the dependence of multiplicity results on the coupling constant $\beta$.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 37, Number 2 (2011), 203-223.

Dates
First available in Project Euclid: 20 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461184783

Mathematical Reviews number (MathSciNet)
MR2849820

Zentralblatt MATH identifier
1255.35101

Citation

Tian, Rushun; Wang, Zhi-qiang. Multiple solitary wave solutions of nonlinear Schrödinger systems. Topol. Methods Nonlinear Anal. 37 (2011), no. 2, 203--223. https://projecteuclid.org/euclid.tmna/1461184783


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