具有有限时滞的测度泛函微分方程的存在性
Existence of Measure FunctionalDifferential Equations withFinite Delay
摘要: 本文研究Banach空间中具有有限时滞的半线性测度泛函微分方程的解的存在性，应用不动点定理和正则函数空间中关于Kuratowski非紧性测度的结论证明了该系统的解的存在性判据，其中不要求系统中线性部分相关联的C0半群的紧性，所得结果是已有文献的补充和推广。最后通过一个例子来说明所得结论的应用。
Abstract: The paper investigates the existence of solutions of semi-linear measure functional differential equations with finite delay in Banach spaces. Some existence criteria of solutions for the system are showed by using a fixed point theorem and the results on Kuratowski measure of non-compactness in the space of regulated functions. The C0 semigroup related to the linear part of the system is not claimed to be compact. The result obtained is the supplement and extension of the existing literature. Finally, the application of the results is elucidated by an example.
文章引用：曹跃菊. 具有有限时滞的测度泛函微分方程的存在性[J]. 理论数学, 2024, 14(11): 25-35. https://doi.org/10.12677/PM.2024.1411371

参考文献

[1] Brogliato, B. and Brogliato, B. (1999) Nonsmooth Mechanics. Vol. 3, Springer-Verlag, 51-93.
[2] Federson, M., G. Mesquita, J. and Slavik, A. (2012) Measure Functional Differential Equations and Functional Dynamic Equations on Time Scales. Journal of Differential Equations, 252, 3816-3847.
https://doi.org/10.1016/j.jde.2011.11.005
[3] Federson, M., Grau, R., Mesquita, J.G. and Toon, E. (2022) Permanence of Equilibrium Points in the Basin of Attraction and Existence of Periodic Solutions for Autonomous Measure Differential Equations and Dynamic Equations on Time Scales via Generalized Odes. Nonlinearity, 35, 3118-3158.
https://doi.org/10.1088/1361-6544/ac6370
[4] Andrade da Silva, F., Federson, M. and Toon, E. (2022) Stability, Boundedness and Controllability of Solutions of Measure Functional Differential Equations. Journal of Differential Equations, 307, 160-210.
https://doi.org/10.1016/j.jde.2021.10.044
[5] Gou, H. and Shi, M. (2024) Monotone Iterative Technique for Multi-Term Time Fractional Measure Differential Equations. Fractional Calculus and Applied Analysis, 27, 1428-1470.
https://doi.org/10.1007/s13540-024-00273-5
[6] Chyba, M., Colombo, R.M., Garavello, M. and Piccoli, B. (2022) Advanced Mathematical Methodologies to Contrast COVID-19 Pandemic. Networks and Heterogeneous Media, 17, i-ii.
https://doi.org/10.3934/nhm.2022020
[7] Weightman, R. and Piccoli, B. (2023). Optimization of Non-Pharmaceutical Interventions for a Mutating Virus. 2023 American Control Conference (ACC), San Diego, CA, 31 May-2 June 2023, 307-312.
https://doi.org/10.23919/acc55779.2023.10156293
[8] Piccoli, B. (2023) Control of Multi-Agent Systems: Results, Open Problems, and Applications. Open Mathematics, 21, Article 20220585.
https://doi.org/10.1515/math-2022-0585
[9] Cao, Y. and Sun, J. (2015) Existence of Solutions for Semilinear Measure Driven Equations. Journal of Mathematical Analysis and Applications, 425, 621-631.
https://doi.org/10.1016/j.jmaa.2014.12.042
[10] Cao, Y. and Sun, J. (2016) Measures of Noncompactness in Spaces of Regulated Functions with Application to Semilinear Measure Driven Equations. Boundary Value Problems, 2016, Article No. 38.
https://doi.org/10.1186/s13661-016-0539-1
[11] Gou, H. and Li, Y. (2021) Existence and Approximate Controllability of Semilinear Measure Driven Systems with Nonlocal Conditions. Bulletin of the Iranian Mathematical Society, 48, 769-789.
https://doi.org/10.1007/s41980-021-00546-2
[12] Pazy, A. (1983) Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer.
[13] Frankova, D. (2019) Regulated Functions with Values in Banach Space. Mathematica Bohemica, 144, 437-456.
https://doi.org/10.21136/mb.2019.0124-19
[14] Liu, L., Guo, F., Wu, C. and Wu, Y. (2005) Existence Theorems of Global Solutions for Nonlinear Volterra Type Integral Equations in Banach Spaces. Journal of Mathematical Analysis and Applications, 309, 638-649.
https://doi.org/10.1016/j.jmaa.2004.10.069

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