Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations

We study a type of third-order linear differential equations with variable and unbounded coefficients, which are defined in an infinite interval. We also consider a non-linear generalization with coefficients that depends on an unknown function. We establish sufficient conditions for the correctness...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 10; p. 1717
Main Authors Ospanov, Myrzagali, Ospanov, Kordan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 17.05.2022
Subjects
correctness
Differential equations
Differential equations, Nonlinear
Food science
Inequality
Linear equations
Mathematical analysis
Mathematical research
maximal regularity estimate
Nonlinear differential equations
Norms
qualitative property of solution
Regularity
third-order differential equation
unbounded coefficient
Germany
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Summary:We study a type of third-order linear differential equations with variable and unbounded coefficients, which are defined in an infinite interval. We also consider a non-linear generalization with coefficients that depends on an unknown function. We establish sufficient conditions for the correctness of this linear equation and the maximal regularity estimate for their solution. Using these results, we prove the solvability of a nonlinear differential equation and estimate the norms of its terms.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10101717