| 单边增长条件下2n阶常微分方程的奇周期解 |
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| 引用本文： | 文乾,李永祥.单边增长条件下2n阶常微分方程的奇周期解[J].四川大学学报(自然科学版),2018,55(6):1167-1170. |
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| 作者姓名： | 文乾 李永祥 |
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| 作者单位： | 西北师范大学数学与统计学院,西北师范大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金(11661071) |
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| 摘 要： | 本文讨论了一类2n阶微分方程周期解的存在性，其中 n 是正整数. 运用Leray-Schauder不动点定理与Fourier分析的方法，在允许非线性项f超线性增长的条件下，本文获得了该方程的奇周期解.
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| 关 键 词： | 单边增长 奇周期解 Leray-Schauder不动点定理 Fourier分析 |
| 收稿时间： | 2018/3/13 0:00:00 |
| 修稿时间： | 2018/5/2 0:00:00 |
Odd periodic solutions for 2n order ordinary differential equations under unilateral growth conditions |
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| WEN Qian and LI Yong-Xiang.Odd periodic solutions for 2n order ordinary differential equations under unilateral growth conditions[J].Journal of Sichuan University (Natural Science Edition),2018,55(6):1167-1170. |
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| Authors: | WEN Qian and LI Yong-Xiang |
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| Institution: | College of Mathematics and Statistics, Northwest Normal University,College of Mathematics and Statistics, Northwest Normal University |
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| Abstract: | In this paper, we discuss the existence of odd periodic solutions for nonlinear 2nth-order differential equations. By applying the Leray-Schauder fixed
point theorem and Fourier analysis method, the results of existence of odd peiodic solutions is obtained under the nonlinearity f satisfies unilateral growth condition. |
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| Keywords: | Unilateral growth Odd periodic solution Leray-Schauder fixed point theorem Fourier series expansion |
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