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| Solutions of a class of higher order variable coefficient homogeneous differential equations | |
| Xu, Tingting1; Deng, Linhua1; Shan, Yulin2; Wan, Miao1; Zhou, Weihong1,3 | |
| 发表期刊 | NETWORKS AND HETEROGENEOUS MEDIA
 |
| 2025 | |
| 卷号 | 20期号:1页码:213-231 |
| DOI | 10.3934/nhm.2025011 |
| 收录类别 | SCI |
| 关键词 | variable coefficient homogeneous differential equations linearly independent solutions rank of coefficient matrices fourth-order and nth-order equations |
| 摘要 | Recently, the variable coefficient homogeneous differential equations (VCHDE) have been widely applied to real-world problems, such as wave propagation and material science. However the exploration and research on higher-order VCHDE is relatively lagging. Given this, this work focuses on the solutions of fourth-order and nth-order VCHDE with polynomial coefficients. By means of the sufficient conditions for the existence of solutions to differential equations, a connection is established between the rank of the variable coefficient matrix and the existence of polynomial particular solutions. The main results show that: (1) the necessary and sufficient conditions for the existence of polynomial particular solutions of fourth-order VCHDE are derived; (2) the necessary and sufficient conditions for the existence of only one polynomial particular solution, or the existence of two, three, or four linearly independent polynomial particular solutions of fourth-order VCHDE are proved; (3) the necessary and sufficient conditions for the existence of only one polynomial particular solution, or the existence of two, three, or four linearly independent polynomial particular solutions of nth-order VCHDE are proved. These results not only extend the class of solvable differential equations, but also provide a new way of thinking about the existence of solutions to VCHDE. |
| 资助项目 | National Nature Science Foundation of China[12463009]; Yunnan Fundamental Research Projects[202301AV070007]; Yunnan Fundamental Research Projects[202401AU070026]; Yunnan Fundamental Research Projects[202401AT070955]; Yunnan Fundamental Research Projects[202401AU070296]; The Yunnan Revitalization Talent Support Program Innovation Team Project[202405AS350012]; Scientific Research Foundation Project of Yunnan Education Department[2023J0624]; Scientific Research Foundation Project of Yunnan Education Department[2024Y469]; Scientific Research Foundation Project of Yunnan Education Department[2025Y0720]; Scientific Research Foundation Project of Yunnan Education Department[2025Y0721]; Scientific Research Foundation Project of Yunnan Education Department[2025J0502]; GHfund A[202407016295] |
| 项目资助者 | National Nature Science Foundation of China[12463009] ; Yunnan Fundamental Research Projects[202301AV070007, 202401AU070026, 202401AT070955, 202401AU070296] ; The Yunnan Revitalization Talent Support Program Innovation Team Project[202405AS350012] ; Scientific Research Foundation Project of Yunnan Education Department[2023J0624, 2024Y469, 2025Y0720, 2025Y0721, 2025J0502] ; GHfund A[202407016295] |
| 语种 | 英语 |
| 学科领域 | 数学 |
| 文章类型 | Article |
| 出版者 | AMER INST MATHEMATICAL SCIENCES-AIMS |
| 出版地 | PO BOX 2604, SPRINGFIELD, MO 65801-2604, UNITED STATES |
| ISSN | 1556-1801 |
| URL | 查看原文 |
| WOS记录号 | WOS:001440277800001 |
| WOS研究方向 | Mathematics |
| WOS类目 | Mathematics, Interdisciplinary Applications |
| 关键词[WOS] | EXISTENCE |
| 引用统计 | |
| 文献类型 | 期刊论文 |
| 版本 | 出版稿 |
| 条目标识符 | http://ir.ynao.ac.cn/handle/114a53/28195 |
| 专题 | 中国科学院天体结构与演化重点实验室 |
| 作者单位 | 1.School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, Yunnan, China; 2.School of Mathematics and Computer Science, Chuxiong Normal University, Chuxiong 675000, Yunnan, China; 3.Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming, Yunnan, 650011, China |
| 推荐引用方式 GB/T 7714 | Xu, Tingting,Deng, Linhua,Shan, Yulin,et al. Solutions of a class of higher order variable coefficient homogeneous differential equations[J]. NETWORKS AND HETEROGENEOUS MEDIA,2025,20(1):213-231. |
| APA | Xu, Tingting,Deng, Linhua,Shan, Yulin,Wan, Miao,&Zhou, Weihong.(2025).Solutions of a class of higher order variable coefficient homogeneous differential equations.NETWORKS AND HETEROGENEOUS MEDIA,20(1),213-231. |
| MLA | Xu, Tingting,et al."Solutions of a class of higher order variable coefficient homogeneous differential equations".NETWORKS AND HETEROGENEOUS MEDIA 20.1(2025):213-231. |
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