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Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations

Author

Listed:
  • Myrzagali Ospanov

    (Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satpaev St., Nur-Sultan 010008, Kazakhstan
    These authors contributed equally to this work.)

  • Kordan Ospanov

    (Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satpaev St., Nur-Sultan 010008, Kazakhstan
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Myrzagali Ospanov & Kordan Ospanov, 2022. "Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations," Mathematics, MDPI, vol. 10(10), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1717-:d:817678
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