poisson system
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2022 ◽  
Vol 359 (10) ◽  
pp. 1279-1293
Author(s):  
Jean Dolbeault ◽  
Rupert L. Frank ◽  
Louis Jeanjean

Author(s):  
Xilin Dou ◽  
xiaoming he

This paper deals with a class of fractional Schr\”{o}dinger-Poisson system \[\begin{cases}\displaystyle (-\Delta )^{s}u+V(x)u-K(x)\phi |u|^{2^*_s-3}u=a (x)f(u), &x \in \R^{3}\\ (-\Delta )^{s}\phi=K(x)|u|^{2^*_s-1}, &x \in \R^{3}\end{cases} \]with a critical nonlocal term and multiple competing potentials, which may decay and vanish at infinity, where $s \in (\frac{3}{4},1)$, $ 2^*_s = \frac{6}{3-2s}$ is the fractional critical exponent. The problem is set on the whole space and compactness issues have to be tackled. By employing the mountain pass theorem, concentration-compactness principle and approximation method, the existence of a positive ground state solution is obtained under appropriate assumptions imposed on $V, K, a$ and $f$.


Author(s):  
Guofeng Che ◽  
Haibo Chen

This paper is concerned with the following Kirchhoff–Schrödinger–Poisson system: [Formula: see text] where constants [Formula: see text], [Formula: see text] and [Formula: see text] are the parameters. Under some appropriate assumptions on [Formula: see text], [Formula: see text] and [Formula: see text], we prove the existence and multiplicity of nontrivial solutions for the above system via variational methods. Some recent results from the literature are greatly improved and extended.


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