| 拟线性Schrdinger-Poisson方程正解、负解、变号解的存在性 |
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| 引用本文： | 王文波,李全清.拟线性Schrdinger-Poisson方程正解、负解、变号解的存在性[J].数学学报,2018,61(4):685-694. |
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| 作者姓名： | 王文波 李全清 |
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| 作者单位： | 1.中科院武汉物理与数学研究所 武汉 430071;中国科学院大学 北京 100049;2.红河学院数学学院 蒙自 661100 |
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| 基金项目： | 云南省地方本科高校（部分）基础研究联合专项；红河学院科研基金博士专项项目（XJ17B11） |
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| 摘 要： | 本文考虑拟线性Schrdinger-Poisson方程{-△u+V(x)u+Φu-1/2△(u~2)u=f(x,u),x∈R~3,-△Φ=u~2,x∈R~3,其中f是一个C~1超线性且次临界的非线性项,V是正的有界位势.利用扰动方法,我们证明了该方程非平凡解、正解、负解、变号解的存在性.
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Existence of Signed and Sign-changing Solutions for Quasilinear Schrödinger-Poisson System |
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| Wen Bo WANG,Quan Qing LI.Existence of Signed and Sign-changing Solutions for Quasilinear Schrödinger-Poisson System[J].Acta Mathematica Sinica,2018,61(4):685-694. |
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| Authors: | Wen Bo WANG Quan Qing LI |
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| Institution: | 1.Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, P. R. China;University of Chinese Academy of Sciences, Beijing 100049, P. R. China;2.Department of Mathematics, Honghe University, Mengzi 661100, P. R. China |
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| Abstract: | We consider the following quasilinear Schrödinger-Poisson system
where f is C1, superlinear and subcritical nonlinearity, V is bounded positive potential. By using the method of perturbation, we prove the system has non-trivial solutions, positive solutions, negative solutions and sign-changing solutions. |
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| Keywords: | Schrödinger-Poisson system sign-changing solutions the method of perturbation |
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