论文标题
具有非主势的Chern-Simons-Schrödinger系统的多峰解决方案
Multi-Peak solutions to Chern-Simons-Schrödinger systems with non-radial potential
论文作者
论文摘要
在本文中，我们考虑了非线性Chern-simons-Schrödinger系统的静态解决方案\ begin {qore} -ihd_0ψ-h^2（d_1d_1+d_2d_2）ψ+vψ= |ψ|^|^{p-2}ψ，\\ \\ \\ \ \ \ \ \ \ \ \ \ \\ partial_0a_1- \ partial_1a_0 = - \ frac 12ih [\ overline inline \ partial_0a_2- \ partial_2a_0 = \ frac 12iH [\overlineψd_1ψ-ψ\ edine {d_1ψ}]，\\ \\ \\ \\ partial_1a_2- \ partial_2a_1 = - \ end {equation}其中$ p> 2 $和非主势$ v（x）$满足某些条件。我们表明，对于每个正整数$ k $，存在$ H_0> 0 $，因此对于$ 0 <h <h_0 $，问题\ eqref {eqabstr {eqabstr}具有非平底静态解决方案$（ψ_h，a_0^h，a_1^h，a_1^h，a_1^h，a_2^h）$。此外，$ψ_h$是一个正面的非radial功能，$ k $阳性峰值，该峰值$ v（x）$ as $ h \ to 0^+$的局部最大点。
In this paper, we consider the existence of static solutions to the nonlinear Chern-Simons-Schrödinger system \begin{equation}\label{eqabstr} \left\{\begin{array}{ll} -ihD_0Ψ-h^2(D_1D_1+D_2D_2)Ψ+VΨ=|Ψ|^{p-2}Ψ,\\ \partial_0A_1-\partial_1A_0=-\frac 12ih[\overlineΨD_2Ψ-Ψ\overline{D_2Ψ}],\\ \partial_0A_2-\partial_2A_0=\frac 12ih[\overlineΨD_1Ψ-Ψ\overline{D_1Ψ}],\\ \partial_1A_2-\partial_2A_1=-\frac12|Ψ|^2,\\ \end{array} \right. \end{equation} where $p>2$ and non-radial potential $V(x)$ satisfies some certain conditions. We show that for every positive integer $k$, there exists $h_0>0$ such that for $0<h<h_0$, problem \eqref{eqabstr} has a nontrivial static solution $(Ψ_h, A_0^h, A_1^h,A_2^h)$. Moreover, $Ψ_h$ is a positive non-radial function with $k$ positive peaks, which approach to the local maximum point of $V(x)$ as $h\to 0^+$.
