无 Lipschitz 假设的脉冲演化方程的非自治性存在与最优控制

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-01-19 DOI:10.1186/s13661-024-01819-5

Lixin Sheng, Weimin Hu, You-Hui Su

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引用次数: 0

摘要

在本文中，我们研究了具有非局部条件的非自主脉冲演化方程的温和解及最优控制的存在性。利用 Schauder 定点定理和演化族理论，我们证明了相关问题的温和解的存在性。此外，在不考虑非线性项的 Lipschitz 连续性的情况下，通过设置两次最小化序列，我们得出了最优控制结果。我们还给出了一个应用这些结果的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption

In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with nonlocal conditions. Using the Schauder’s fixed-point theorem as well as the theory of evolution family, we prove the existence of mild solutions for the concerned problem. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. An example is given of the application of the results.

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.