| 分数阶自治Kirchhoff方程径向变号解的存在性 |
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| 引用本文： | 张丹丹,丁凌.分数阶自治Kirchhoff方程径向变号解的存在性[J].四川大学学报(自然科学版),2020,57(2):243-246. |
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| 作者姓名： | 张丹丹 丁凌 |
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| 作者单位： | 湖北文理学院数学与统计学院,襄阳441053;湖北文理学院数学与统计学院,襄阳441053 |
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| 基金项目： | 国家自然科学基金(11861021);湖北省教育厅科研研究计划项目(B2018156) |
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| 摘 要： | 本文考虑全空间上一类分数阶自治Kirchhoff方程变号解的存在性.首先,我们证明了分数阶自治的Kirchhoff方程在适当条件下与一个分数阶自治Schrdinger系统等价;然后,利用分数阶自治Schrdinger方程的径向变号解的存在性结果,我们证明了分数阶自治的Schrdinger系统的解的存在性;最后,我们得到了分数阶自治的Kirchhoff方程径向变号解的存在性.
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| 关 键 词： | 分数阶 Kirchhoff方程 自治Schr?dinger系统 变号解 |
| 收稿时间： | 2019/3/11 0:00:00 |
| 修稿时间： | 2019/5/8 0:00:00 |
Existence of radial sign-changing solution for a fractional autonomous Kirchhoff equation |
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| ZHANG Dan-dan and DING Ling.Existence of radial sign-changing solution for a fractional autonomous Kirchhoff equation[J].Journal of Sichuan University (Natural Science Edition),2020,57(2):243-246. |
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| Authors: | ZHANG Dan-dan and DING Ling |
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| Institution: | Hubei University of Arts and Scince,Hubei University of Arts and Scince |
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| Abstract: | The existence of sign-changing solutions for a fractional autonomous Kirchhoff equation is considered in the whole space. We prove that this equation is equivalent to a fractional autonomous Schr&odinger system under appropriate conditions. Then, by using the existence of radial sign-changing solution of the fractional autonomous Schrodinger equation, the existence of solutions for the fractional autonomous Schrodinger system is proved. The existence of radial sign-changing solution for the fractional autonomous Kirchhoff equation is obtained as well. |
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| Keywords: | Fractional order Kirchhoff equations autonomous Schrö dinger system a sign-changing solution |
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