Elliptic Systems with a Partially Sublinear Local Term

Journal of Mathematical Study
Vol. 48 No. 3 (2015), pp. 290-305
DOI: 10.4208/jms.v48n3.15.07
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Author(s)
,
1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China
2 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Abstract

Let $1$$\begin{cases} -\Delta u+[V(x)-(\omega+e\phi)^2]u=K(x)|u|^{p-2}u \  \  \ {\rm in}  \ \mathbb{R}^3,\\ -\Delta\phi+e^2u^2\phi=-e\omega u^2 \  \  \ {\rm in} \ \mathbb{R}^3 \end{cases}$$ where $ω, e > 0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results.

Keywords
Schrödinger-Poisson system Klein-Gordon-Maxwell system infinitely many solutions.
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