@Article{JMS-48-3,
author = {Yongtao, Jing and Zhaoli, Liu},
title = {Elliptic Systems with a Partially Sublinear Local Term},
journal = {Journal of Mathematical Study},
year = {2015},
volume = {48},
number = {3},
pages = {290--305},
abstract = {<p style="text-align: justify;">Let $1&lt;p&lt;2$. Under some assumptions on $V,$ $K,$ existence of infinitely many
solutions $(u,\phi) ∈ H^1(\mathbb{R}^3) \times D^{1,2}(\mathbb{R}^3)$ is proved for the Schrödinger-Poisson system $$\begin{cases} -\Delta u+V(x)u+\phi u=K(x)|u|^{p-2}u \&nbsp; \&nbsp; \ {\rm in}&nbsp; \ \mathbb{R}^3,\\ -\Delta\phi=u^2 \&nbsp; \&nbsp; \ {\rm in} \ \mathbb{R}^3 \end{cases}$$ as well as for the Klein-Gordon-Maxwell system&nbsp;<span style="text-align: justify;">$$\begin{cases} -\Delta u+[V(x)-(\omega+e\phi)^2]u=K(x)|u|^{p-2}u \&nbsp; \&nbsp; \ {\rm in}&nbsp; \ \mathbb{R}^3,\\ -\Delta\phi+e^2u^2\phi=-e\omega u^2 \&nbsp; \&nbsp; \ {\rm in} \ \mathbb{R}^3 \end{cases}$$</span>&nbsp;where $ω, e &gt; 0.$ This is in sharp contrast to D&#39;Aprile and Mugnai&#39;s non-existence results.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v48n3.15.07},
url = {https://global-sci.com/article/87831/elliptic-systems-with-a-partially-sublinear-local-term}
}