| 一类非线性分数阶薛定谔-泊松系统非零解的存在性 |
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| 引用本文： | 张鹏,韩志清.一类非线性分数阶薛定谔-泊松系统非零解的存在性[J].数学研究及应用,2022,42(2):162-172. |
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| 作者姓名： | 张鹏 韩志清 |
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| 作者单位： | 大连理工大学数学科学学院, 辽宁 大连 116024 |
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| 摘 要： | 本文研究了分数阶薛定谔-泊松系统$$\left\{\begin{array}{l}(-\Delta)^su+u+\phi u=\lambda f(u)\ \text {in} \ \mathbb {R}^3, \\ (-\Delta)^{\alpha}\phi =u^2\ \text {in} \ \mathbb {R}^3\emph{},\end{array}\right. $$ 非零解的存在性, 其中$s\in (\frac{3}{4},1), \alpha\in(0,1),\lambda$ 是正参数, $(-\Delta)^s,(-\Delta)^{\alpha}$是分数阶拉普拉斯算子. 在一定的假设条件下, 利用扰动法和Morse迭代法, 得到了系统至少一个非平凡解.
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| 关 键 词： | 分数阶薛定谔-泊松系统 非平凡解 扰动法 Morse迭代法 |
| 收稿时间： | 2021/1/31 0:00:00 |
| 修稿时间： | 2021/5/20 0:00:00 |
Existence of Nontrivial Solutions for a Class of Nonlinear Fractional Schr\"{o}dinger-Poisson System |
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| Peng ZHANG,Zhiqing HAN.Existence of Nontrivial Solutions for a Class of Nonlinear Fractional Schr\"{o}dinger-Poisson System[J].Journal of Mathematical Research with Applications,2022,42(2):162-172. |
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| Authors: | Peng ZHANG Zhiqing HAN |
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| Institution: | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | {R}^3\emph{},\end{array}\right.$$ where $s\in (\frac{3}{4},1), \alpha\in(0,1),\lambda$ is a positive parameter, $(-\Delta)^s,(-\Delta)^{\alpha}$ are fractional Laplacian operators. Under certain assumptions on $f$, we obtain the existence of at least one nontrivial solution of the system by using the methods of perturbation and Moser iterative method. |
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| Keywords: | fractional Schr\"{o}dinger-Poisson system nontrivial solution perturbation method Moser iterative method |
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