Estimates for the Diameters of the Set of Solutions to a Nonlinear Differential Equation With Unbounded Coefficients
Ospanov K. Ospanov M.
30 March 2025John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2025#48Issue 56103 - 6109 pp.
In this paper, we prove some estimates of the distribution functions of the Kolmogorov diameters of solutions set to one class of the third-order nonlinear differential equations with variable coefficients. The equation is defined on the entire real axis, and its coefficients are unbounded functions. Previously, such equations were studied in the case where their intermediate coefficients are equal to zero, and the junior coefficient does not change sign. Sufficient conditions for the existence of a weak solution are also obtained, and under some restrictions on the oscillation of the intermediate coefficient, the maximal regularity of the solution is proved in the paper. In the proofs of the theorems are use the results of the authors obtained in the case of a linear differential equation of the third order (Ospanov & Ospanov, 2024), and Schauders fixed point theorem.
Kolmogorov diameter , maximal regularity , nonlinear differential equation , singularity , solvability , unbounded coefficient
Text of the article Перейти на текст статьи
Faculty of Mathematics and Mechanics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Faculty of Mathematics and Mechanics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026