# Cauchy problem for class of second order nonlinear ordinary differential equations

• A. B. Tungatarov Казахский Национальный Университет имени аль-Фараби

### Abstract

In the work for class of second order nonlinear ordinary differential equations with variable coefficients in the neighbourhood of a point x0 of real line the existence of continuous solutions of Cauchy problem is proved. Constructed by the author the general solution of the second order linear differential equations with variable coefficients and Schauder’s principle for fixed point are used for proving of the Peano’s theorem. Construction method of the general solution of linear differential equations of the second order with variable coefficients and the general solution can be useful for solving of different applied problems of natural science. For simplicity, the coefficient and nonlinear part of ordinary differential equation of the second order are taken of class of continuous functions. It can be taken of class measurable and essentially limited functions. It is easy to verify, that the results of the work are true in this case.

### References

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[3] Tungatarov A., Akhmed-Zaki D.K. Cauchy problem for one class of ordinary differential equations. // International Journal of Mathematical Analysis, –2012, – v. 6, № 14, –P. 695-699.

[4] Тунгатаров А., Ахмед-Заки Д.К. Задача Коши для одного класса обыкновенных дифференциальных уравнений второго порядка // Вестник КазНУ, сер. мат., мех., инф. – 2011. –№ 3 (70). – С. 31-35.
How to Cite
TUNGATAROV, A. B.. Cauchy problem for class of second order nonlinear ordinary differential equations. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 76, n. 1, p. 22-28, feb. 2015. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/83>. Date accessed: 23 may 2019.
Citation Formats
Section
Mechanics, Mathematics, Computer Science

### Keywords

Nonlinear equation; Peano’s theorem; continuous solution; Schauder’s principle; general solution.