Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations

Ospanov, Myrzagali N.; Ospanov, Kordan N.

doi:10.3390/math10101717

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…Note that the general differential equation of the third order with smooth coefficients can be reduced to the form (). In the case that the coefficients

ρ_{1}

ρ_{2}

are constant, some correctness results for Equation () are given in [10]. For the first time, coercive estimates for differential equations with nonsmooth coefficients were obtained in [11].…”

Section: Introductionmentioning

confidence: 99%

The maximal regularity of the third‐order differential equation and its applications

Ospanov,

Ospanov

2024

Math Methods in App Sciences

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In this work, we study the solvability and maximal regularity questions for the singular third‐order differential equation with unbounded coefficients and some applications. Unlike previously studied cases, the leading and intermediate coefficients of this equation can grow independently. We obtain sufficient coefficient conditions for correctness of this equation and compactness for inverse of the corresponding differential operator. We also prove the maximal regularity estimate for a generalized solution. Using these results, we obtain upper and lower estimates for the number of Kolmogorov ‐diameters of the set associated with the linear Korteweg–de Vries equation's solutions. We give an example and show that from the above inequalities follow two‐sided estimates of the Kolmogorov ‐diameters.

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“…Note that the general differential equation of the third order with smooth coefficients can be reduced to the form (). In the case that the coefficients

ρ_{1}

ρ_{2}

are constant, some correctness results for Equation () are given in [10]. For the first time, coercive estimates for differential equations with nonsmooth coefficients were obtained in [11].…”

Section: Introductionmentioning

confidence: 99%

The maximal regularity of the third‐order differential equation and its applications

Ospanov,

Ospanov

2024

Math Methods in App Sciences

Self Cite

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Medical and social problems of optimizing the nutrition of children and adolescents under the conditions of today

Solovyova

2022

Российский Вестник Гигиены

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The article reviews publications devoted to the issue of optimization of nutrition of children and adolescents including school nutrition, various ways of formation of eating habits, succession of home and school nutrition, nutrition of children with alimentary-dependent diseases and children who go in for sports, quality of raw materials and products for school nutrition, and nutrition using new products. The information was searched for with eLIBRARY.RU, PUBMED, Web of Science and Scopus information portals and platforms from 2007 to 2021. Publications related to the issue were assessed while studying at school and during distance learning. Modern issues of nutrition of schoolchildren such as disturbances of alimentary behavior and underdeveloped skills of nutritional culture, dietary habits of schoolchildren with alimentary-dependent diseases and approaches to nutrition optimization at educational institutions are highlighted. The ways of prevention of alimentary-dependent diseases are estimated by way of inclusion of functional products into the diet of schoolchildren. Principal methodical and regulatory documents that can help reduce risks of alimentary-dependent diseases are mentioned. Pressing trends of researches regarding the reviewed topic were suggested to preserve health of schoolchildren as far as healthy nutrition goes.

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Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations

Cited by 2 publications

References 18 publications

The maximal regularity of the third‐order differential equation and its applications

The maximal regularity of the third‐order differential equation and its applications

Medical and social problems of optimizing the nutrition of children and adolescents under the conditions of today

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