Document Type


Source Publication Title

Technical Report 18


As is well-known [3] the method of variation of parameters is a very useful tool in studying the properties of solutions of perturbed differential equations. Extending the classical variation of constants formula for linear systems, Alekseev [1] obtained a variation of constants formula for nonlinear systems. In [2], Lakshmikantham developed a nonlinear variation of constants formula for a scalar differential equation whose unperturbed term is of variable separable type, under rather mild assumptions. In this paper, we wish to study the general problem under weaker assumptions. Our approach is parallel to the classical one and yields two different formulas, one of which is shown to be equivalent to the Alekseev's formula under additional restrictions. Also, the formula given in [2] is shown to be a consequence of our results. To illustrate the flexibility of the results derived, we give as applications results on stability and asymptotic equilibrium.


Mathematics | Physical Sciences and Mathematics

Publication Date




Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.