Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations

Myrzagali N. Ospanov, Kordan Nauryzkhanovich Ospanov

2022

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DOI 10.3390/math10101717
Data confidence 70 medium
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Abstract

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.