下临界Choquard型线性耦合系统基态解的存在性
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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。
To the best of our knowledge, there is few result about linearly coupled systems of Choquard type with the lower critical up to now. The existence of ground state solutions for a class of Choquard-type linear coupled systems with lower critical exponents is studied by variational methods. It is a promotion and supplement to the previous research results.
To the best of our knowledge, there is few result about linearly coupled systems of Choquard type with the lower critical up to now. The existence of ground state solutions for a class of Choquard-type linear coupled systems with lower critical exponents is studied by variational methods. It is a promotion and supplement to the previous research results.
引文
[1] LIEB E H.Existence and uniqueness of the minimizing solution of Choquard?s 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.
[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.