English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the existence of static solutions to the nonlinearChern-Simons-Schr\"odinger system \begin{equation}\label{eqabstr}\left\{\begin{array}{ll}-ihD_0\Psi-h^2(D_1D_1+D_2D_2)\Psi+V\Psi=|\Psi|^{p-2}\Psi,\\\partial_0A_1-\partial_1A_0=-\frac12ih[\overline{\Psi}D_2\Psi-\Psi\overline{D_2\Psi}],\\\partial_0A_2-\partial_2A_0=\frac12ih[\overline{\Psi}D_1\Psi-\Psi\overline{D_1\Psi}],\\\partial_1A_2-\partial_2A_1=-\frac12|\Psi|^2,\\ \end{array} \right.\end{equation} where $p>2$ and non-radial potential $V(x)$ satisfies somecertain 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 nontrivialstatic solution $(\Psi_h, A_0^h, A_1^h,A_2^h)$. Moreover, $\Psi_h$ is apositive non-radial function with $k$ positive peaks, which approach to thelocal maximum point of $V(x)$ as $h\to 0^+$.

Multi-Peak solutions to Chern-Simons-Schr\"odinger systems with non-radial potential