Monotone iterative technique for evolution equations with delay and nonlocal conditions in ordered Banach space

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2023-11-14 DOI:10.1080/17442508.2023.2280693

Haide Gou

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引用次数: 0

Abstract

AbstractIn this paper, based on monotone iterative method in the presence of the lower and upper solutions, we investigate the existence and uniqueness of the S-asymptotically ω-periodic mild solutions to a class of nonlocal problems of evolution equations with delay in ordered Banach spaces. Firstly, we introduce the concept of lower S-asymptotically ω-periodic solution and upper S-asymptotically ω-periodic solution. Secondly, we construct monotone iterative method in the presence of the lower and upper solutions to evolution equations with delay, and obtain the existence of maximal and minimal S-asymptotically ω-periodic mild solutions for the mentioned system under wide monotone conditions and noncompactness measure condition of nonlinear term. Finally, as the application of abstract results, an example is given to illustrate our main results.Keywords: Evolution equationsdelaynonlocal problemsmonotone iterative techniqueC0-semigroupS-asymptotically ω-periodic mild solutionsMathematics Subject Classifications: 35R1235K9047D06 Data availability statementMy manuscript has no associate data.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was supported by the National Natural Science Foundation of China [No. 12061062], Science Research Project for Colleges and Universities of Gansu Province [No. 2022A-010].

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有序Banach空间中时滞非局部条件演化方程的单调迭代技术

摘要本文利用有上下解存在的单调迭代方法，研究了有序Banach空间中一类时滞演化方程非局部问题s渐近ω-周期温和解的存在唯一性。首先，我们引入了下s渐近ω周期解和上s渐近ω周期解的概念。其次，构造了具有时滞演化方程上下解存在的单调迭代方法，得到了该系统在广义单调条件和非线性项的非紧性测度条件下最大最小s渐近ω周期温和解的存在性。最后，作为抽象结果的应用，给出了一个例子来说明我们的主要结果。关键词:进化方程;时滞非局部问题;单调迭代技术;0-半群;渐近ω-周期温和解;数学学科分类:35R1235K9047D06数据可用性声明我的稿件没有关联数据。披露声明作者未报告潜在的利益冲突。本研究由国家自然科学基金资助[No. 1];12061062]，甘肃省高等学校科研项目[No. 12061062];2022 - 010年)。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.