Ground states and high energy solutions of the planar Schr\"odinger-Poisson system

15 Mar 2017 Du Miao Weth Tobias

In this paper, we are concerned with the Schr\"{o}dinger-Poisson system $$(0.1)\qquad -\Delta u + u +\phi u = |u|^{p-2}u \quad \text{in}\ \mathbb{R}^{d},\qquad \Delta \phi= u^{2} \quad \text{in}\ \mathbb{R}^{d}.$$ Due to its relevance in physics, the system has been extensively studied and is quite well understood in the case $d \ge 3$... (read more)

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