《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (8): 62-67.doi: 10.6040/j.issn.1671-9352.0.2018.670
王培婷,李安然*,魏重庆
摘要： 到目前为止,关于带有下临界指数的Choquard型线性耦合系统的研究还很少。利用变分法研究一类带有下临界指数的Choquard型线性耦合系统基态解的存在性。所做研究是对以往相关研究成果的推广和补充。
中图分类号:
| [1] LIEB E H. Existence and uniqueness of the minimizing solution of Choquards nonlinear equation[J]. Studies in Applied Mathematics, 1976/1977, 57(2):93-105. [2] MOROZ V, VAN SCHAFTINGEN J. Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics[J]. Journal of Functional Analysis, 2013, 265(2):153-184. [3] VAN SCHAFTINGEN J, XIA J K. Choquard equations under confining external potentials[J]. NoDEA Nonlinear Differential Equations Applications, 2017, 24(1):24. [4] VAN SCHAFTINGEN J, XIA J K. Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent[J]. Journal of Mathematical Analysis and Applications, 2018, 464(2):1184-1202. [5] CHEN P, LIU X. Ground states of linearly coupled systems of Choquard type[J]. Applied Mathematics Letters, 2018, 84:70-75. [6] BARTSCH T, WANG Z Q. Existence and multiplicity results for some superlinear elliptic problems on RN[J]. Communciations in Partial Differential Equations, 1995, 20(9/10):1725-1741. [7] LIEB E H, LOSS M. Analysis[M] // Graduate Studies in Mathematics: Vol 14. Providence, Rhode Island: American Mathematical Society, 2001: 106-110. |
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