{"title":"Estimates for the Diameters of the Set of Solutions to a Nonlinear Differential Equation With Unbounded Coefficients","authors":"Kordan Ospanov, Myrzagali Ospanov","doi":"10.1002/mma.10658","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this paper, we prove some estimates of the distribution functions of the Kolmogorov diameters of solution's set to one class of the third-order nonlinear differential equations with variable coefficients. The equation is defined on the entire real axis, and its coefficients are unbounded functions. Previously, such equations were studied in the case where their intermediate coefficients are equal to zero, and the junior coefficient does not change sign. Sufficient conditions for the existence of a weak solution are also obtained, and under some restrictions on the oscillation of the intermediate coefficient, the maximal regularity of the solution is proved in the paper. In the proofs of the theorems are use the results of the authors obtained in the case of a linear differential equation of the third order (Ospanov & Ospanov, 2024), and Schauder's fixed point theorem.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6103-6109"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10658","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove some estimates of the distribution functions of the Kolmogorov diameters of solution's set to one class of the third-order nonlinear differential equations with variable coefficients. The equation is defined on the entire real axis, and its coefficients are unbounded functions. Previously, such equations were studied in the case where their intermediate coefficients are equal to zero, and the junior coefficient does not change sign. Sufficient conditions for the existence of a weak solution are also obtained, and under some restrictions on the oscillation of the intermediate coefficient, the maximal regularity of the solution is proved in the paper. In the proofs of the theorems are use the results of the authors obtained in the case of a linear differential equation of the third order (Ospanov & Ospanov, 2024), and Schauder's fixed point theorem.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
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