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

The aim of this paper is to study the multiplicity of solutions for thefollowing Kirchhoff type elliptic systems  \begin{eqnarray*}  \left\{ \arraycolsep=1.5pt  \begin{array}{ll}  -m\left(\sum^k_{j=1}\|u_j\|^2\right)\Deltau_i=\frac{f_i(x,u_1,\ldots,u_k)}{|x|^\beta}+\varepsilon h_i(x),\ \ & \mbox{in}\\ \Omega, \ \ i=1,\ldots,k ,\\[2mm]  u_1=u_2=\cdots=u_k=0,\ \ & \mbox{on}\ \ \partial\Omega,  \end{array}  \right.  \end{eqnarray*} where $\Omega$ is a bounded domain in $\mathbb{R}^2$containing the origin with smooth boundary, $\beta\in [0,2)$, $m$ is aKirchhoff type function, $\|u_j\|^2=\int_\Omega|\nabla u_j|^2dx$, $f_i$ behaveslike $e^{\beta s^2}$ when $|s|\rightarrow \infty$ for some $\beta>0$, and thereis $C^1$ function $F: \Omega\times\mathbb{R}^k\to \mathbb{R}$ such that$\left(\frac{\partial F}{\partial u_1},\ldots,\frac{\partial F}{\partialu_k}\right)=\left(f_1,\ldots,f_k\right)$, $h_i\in\left(\big(H^1_0(\Omega)\big)^*,\|\cdot\|_*\right)$. We establish sufficientconditions for the multiplicity of solutions of the above system by usingvariational methods with a suitable singular Trudinger-Moser inequality when$\varepsilon>0$ is small.

On a nonhomogeneous Kirchhoff type elliptic system with the singular Trudinger-Moser growth