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 $\beta$.
Citation
Rushun Tian. Zhi-qiang Wang. "Multiple solitary wave solutions of nonlinear Schrödinger systems." Topol. Methods Nonlinear Anal. 37 (2) 203 - 223, 2011.
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