期刊
NONLINEARITY
卷 30, 期 9, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/aa7eac
关键词
Schrodinger-Poisson system; logarithmic convolution potential; ground state solutions; variational methods
资金
- Natural Science Foundation of China [71690242, 91546118, 11571140, 11671077, 11601204]
- Major Project of Natural Science Foundation of Jiangsu Province Colleges and Universities [14KJA110001]
In this paper, we are concerned with the Schrodinger-Poisson system {-Delta u + u + empty set u = vertical bar u vertical bar(p-2)u in R-d, Delta empty set - u(2) in R-d. (0.1) Due to its relevance in physics, the system has been extensively studied and is quite well understood in the case d >= 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 S and Weth T (2016 On the planar Schrdinger-Poisson system Ann. Inst. Henri Poincare 33 169-97) 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 Cingolani S and Weth T (2016 On the planar Schrodinger-Poisson system Ann. Inst. Henri Poincare 33 169-97) is restricted to the case p >= 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.
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