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- W2962839220 abstract "In this paper, we are concerned with the Schr{o}dinger-Poisson system begin{equation} (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}. end{equation} Due to its relevance in physics, the system has been extensively studied and is quite well understood in the case $d ge 3$. In contrast, much less information is available in the planar case $d=2$ which is the focus of the present paper. It has been observed by Cingolani and the second author cite{Cingolani-Weth-2016} that the variational structure of $(0.1)$ differs substantially in the case $d=2$ and leads to a richer structure of the set of solutions. However, the variational approach of cite{Cingolani-Weth-2016} is restricted to the case $p ge 4$ which excludes some physically relevant exponents. In the present paper, we remove this unpleasant restriction and explore the more complicated underlying functional geometry in the case $2<p<4$ with a different variational approach." @default.
- W2962839220 created "2019-07-30" @default.
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- W2962839220 date "2017-08-14" @default.
- W2962839220 modified "2023-10-04" @default.
- W2962839220 title "Ground states and high energy solutions of the planar Schrödinger–Poisson system" @default.
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- W2962839220 doi "https://doi.org/10.1088/1361-6544/aa7eac" @default.
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