| A. Gritsans and F. Sadyrbaev. Explicit solutions of non-autonomous Emden - Fowler type equations |
| We consider the nonlinear equations of the form $x'' = - q(t) |x|^{2\varepsilon}x, \quad '=\frac{d}{dt}, \quad \varepsilon > 0, \quad q \in C (R, (0, +\infty)),$ where $q(t)$ are some specific $t$-dependent functions such that explicit formulas for solutions can be given. We study properties of solutions, construct principal and non-principal (in the sense of Hartman) solutions and compute the characteristic numbers introduced by Nehari. |