Year: 2015
Author: Yongtao Jing, Zhaoli Liu
Journal of Mathematical Study, Vol. 48 (2015), Iss. 3 : pp. 290–305
Abstract
Let $1<p<2$. 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 $$\begin{cases} -\Delta u+V(x)u+\phi u=K(x)|u|^{p-2}u \ \ \ {\rm in} \ \mathbb{R}^3,\\ -\Delta\phi=u^2 \ \ \ {\rm in} \ \mathbb{R}^3 \end{cases}$$ as well as for the Klein-Gordon-Maxwell system $$\begin{cases} -\Delta u+[V(x)-(\omega+e\phi)^2]u=K(x)|u|^{p-2}u \ \ \ {\rm in} \ \mathbb{R}^3,\\ -\Delta\phi+e^2u^2\phi=-e\omega u^2 \ \ \ {\rm in} \ \mathbb{R}^3 \end{cases}$$ where $ω, e > 0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v48n3.15.07
Journal of Mathematical Study, Vol. 48 (2015), Iss. 3 : pp. 290–305
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Schrödinger-Poisson system Klein-Gordon-Maxwell system infinitely many solutions.