一类Schr?dinger-Poisson系统非平凡解的存在性
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摘要
利用变分方法和临界点理论,研究了一类Schr?dinger-Poisson系统,其中泊松项为更一般的形式,通过给非线性项加拟临界增长和AR条件,得到了该系统非平凡解的存在性。补充和推广了以往研究Schr?dinger-Poisson系统的相关结果。
We investigate a class of Schr?dinger-Poisson systems, by means of variational method and critical point theory. Here, the Poisson term is a more general form. By adding quasi-critical growth and AR conditions to the nonlinear term, we prove the existence of nontrival solution of the system. The result supplement and promote the previous resluts on the Schr?dinger-Poisson systems.
We investigate a class of Schr?dinger-Poisson systems, by means of variational method and critical point theory. Here, the Poisson term is a more general form. By adding quasi-critical growth and AR conditions to the nonlinear term, we prove the existence of nontrival solution of the system. The result supplement and promote the previous resluts on the Schr?dinger-Poisson systems.
引文
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[7] 毛安民,李安然.薛定谔方程及薛定谔-麦克斯韦方程的多解[J].数学学报,2012,55(3):425-436.MAO Anmin,LI Anran.Multiplicity of solutions for a Schr?dinger equation and a Schr?dinger-Maxwell equation[J].Acta Mathematica Sinica,Chinese Series,2012,55(3):425-436.
[8] WILLE M.Minimax theorems:progress in nonlinear differential equations and their applications[M].Boston:Birkh?user,1996.
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[2] NIER F.A stationary Schr?dinger-Poisson system arising from the modelling of electronic devices[J].Forum Mathematicum,1990,2(5):489-510.
[3] LI Fuyi,LI Yuhua,SHI Junping.Existence of positive solutions to Schr?dinger-Poisson type systems with critical exponent[J].Communications in Contemporary Mathematics,2014,16(6):1-29.
[4] LI Yuhua,LI Fuyi,SHI Junping.Existence and multiplicity of positive solutions to Schr?dinger-Poisson type systems with critical nonlocal term[J].Calculus of Variations,2017,56(134):1-17.
[5] MAO Anmin,YANG Lijuan,QIAN Aixia,et al.Existence and concentration of solutions of Schr?dinger-Poisson system[J].Applied Mathematics Letters,2017,68:8-12.
[6] 叶一蔚,唐春雷.带有超线性项或次线性项的Schr?dinger-Poisson系统解的存在性和多重性[J].数学物理学报,2015,35A(4):668-682.YE Yiwei,TANG Chunlei.Existence and multiplicity results for Schr?dinger-Poisson system with superlinear or sublinear terms[J].Acta Mathematica Scientia,2015,35(A):668-682.
[7] 毛安民,李安然.薛定谔方程及薛定谔-麦克斯韦方程的多解[J].数学学报,2012,55(3):425-436.MAO Anmin,LI Anran.Multiplicity of solutions for a Schr?dinger equation and a Schr?dinger-Maxwell equation[J].Acta Mathematica Sinica,Chinese Series,2012,55(3):425-436.
[8] WILLE M.Minimax theorems:progress in nonlinear differential equations and their applications[M].Boston:Birkh?user,1996.
[9] BARTSCH T,WANG Zhiqiang.Existence and multiple results for some superlinear elliptic problems on RN[J].Communication in Partial Differential Equations,1995,20:1725-1741.
[10] RABINOWITZ P H.Minimax methods in critical point theory with applications to differential equations[M].Providence,RI:AMS,1986.
[11] BARTOLO P,BENCI V,FORTUNATO D.Abstract critical point theorems and applications to some nonlinear problem with strong resonance at infinity[J].Nonlinear Analysis,1983,7:981-1012.