Applied Mathematics and Mechanics

, Volume 3, Issue 4, pp 541–547

# The boundedness and asymptotic behavior of solutions of differential system of second-order with variable coefficients

Article

## Abstract

In this paper, the differential system of second-order with variable coefficients is studied, and some criteria of the boundedness and asymptotic behavior for solutions are given. Consider a system of differential equations
$$\left. {\begin{array}{*{20}c} {\frac{{dx_1 }}{{dt}} = p_{11} (t)x_1 + p_{12} (i)x_2 } \\ {\frac{{dx_2 }}{{dt}} = p_{21} (t)x_1 + p_{22} (t)x_2 } \\ \end{array} } \right\}$$
(0.1)
Now we study the boundedness and asymptotic behavior of its solutions. In the case of pij(t)being periodic functions, it was investigated by Burdina[1]; in the case of pij(t) being arbitrary functions, it has not been investigated yet. Besides, the method used by Burdina is only appropriate for the former but not for the latter case. In this paper we shall give a method which is appropriate for both cases.

## Keywords

Differential Equation Mathematical Modeling Asymptotic Behavior Industrial Mathematic Periodic Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. (1).
Burdina, V.I.,A Criterion of Boundedness for Solutions of a System of Differential Equations of Second Order with Periodic Coefficients, Doklady Akad. Nauk SSSR, (N.S.) 90 (1953). (in Russian)Google Scholar
2. (2).
Borg, G.,On a Liapounoff Criterion of Stability, Amer. Jour. of Math. V. 71, No. 1, (1949).Google Scholar
3. (3).
Sansone, G.,Equazioni Differenziali nel Campo Reale, 2 vols., second edit. Zanichelli (1948). (Russian version) Vol. 2., Moscow, 1953)Google Scholar