The Asymptotic Properties of Rapidly Varying Solutions of Second Order Differential Equations with Regularly and Rapidly Varying Nonlinearities

The investigations of second order differential equations play an important role in the development of the qualitative theory of differential equations. Such equations have a lot of applications in different fields of science. Many results have been obtained for equations with power nonlinearities. But in practice we often deal with differential equations not only with power nonlinearities but also with exponential nonlinearities. It happens, for example, when we study the distribution of electrostatic potential in a cylindrical volume of plasma of products of burning. The corresponding equation may be reduced to the following one y′′ = α0p(t)e σy|y′|λ.