Multiple solitary wave solutions of nonlinear Schrödinger systems
Keywords
Nonlinear Schrödinger system, Nehari manifold, a $Z_N$-index theoryAbstract
Consider the $N$-coupled nonlinear elliptic system $$ \cases \displaystyle -\Delta U_j+ U_j=\mu U_j^3+\beta U_j\sum_{k\neq j} U_k^2 \quad \text{in } \Omega,\\ U_j> 0 \quad\text{in } \Omega,\quad U_j=0 \quad \text{on } \partial\Omega,\ j=1, \ldots, N. \endcases \tag P $$ 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 $\beta$.Downloads
Published
2011-04-23
How to Cite
1.
TIAN, Rushun and WANG, Zhi-Qiang. Multiple solitary wave solutions of nonlinear Schrödinger systems. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 37, no. 2, pp. 203 - 223. [Accessed 23 April 2024].
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