Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations

Myrzagali Ospanov and Kordan Ospanov
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Myrzagali Ospanov: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satpaev St., Nur-Sultan 010008, Kazakhstan
Kordan Ospanov: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satpaev St., Nur-Sultan 010008, Kazakhstan

Mathematics, 2022, vol. 10, issue 10, 1-11

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.

Keywords: third-order differential equation; unbounded coefficient; correctness; maximal regularity estimate; qualitative property of solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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