关于存在某种基于冲动的Sobolev类型模糊整微方程的研究
B Radhakrishnan1, M Nagarajan2, P Anukokila3
1Department of Mathematics, PSG College of Technology, Coimbatore-04, TamilNadu, India. radhakrishnanb1985@gmail.com.
BMC research notes
|January 30, 2024
概括
这项研究证明了使用冲动和半组理论解决抽象微分方程和整微分方程的存在. 该研究还应用了模糊数和巴纳赫固定点方法来分析这些复杂的数学模型.
科学领域:
- 数学 数学 是一个数学.
- 应用数学 应用数学 应用数学
- 微分方程 微分方程 微分方程
背景情况:
- 研究抽象微分方程和整微分方程,特别是索波列夫式的方程.
- 解决了复杂数学方程中分析结果的需求.
研究的目的:
- 证明抽象微分方程和整微分方程的解的存在.
- 用半组理论和巴纳赫固定点方法进行分析.
- 通过在特定范围内使用模糊数字来检查发现.
主要方法:
- 使用冲动和非局部约束来建立存在定理.
- 杆半组理论,包括常数公式的变体.
- 应用巴纳赫定点定理与模糊的数字 (正常,凸,上半连续,紧支持).
主要成果:
- 证明了研究的抽象方程的解决方案的存在.
- 提供来自半组理论的分析结果.
- 在模糊数论的框架内分析结果.
结论:
- 证实了用于证明解决方案存在的方法的适用性.
- 突出了模糊数在分析此类微分方程中的实用性.
- 通过说明性描述,提供了对原则的全面理解.
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