On the Dynamics of the Generalized Emden–Fowler Equation

Abstract

Abstract We present some recent results dealing with the qualitative behavior of solutions of the quasilinear second order differential equation where a, b are positive continuous real functions, and Φ j (u) = |u| j–2 u, j > 1. Following a classification of solutions, proposed in the linear case in [Marini and Zezza, J. Diff. Equat. 28: 1–17, 1978], we divide all the solutions of (∗) with respect to their asymptotic behavior into two classes. The existence and uniqueness is considered: a topological approach is employed and a fixed point result for operators associated to boundary value problems on a half-line is used. In addition, some asymptotic estimates are presented and the convergence of solutions to zero as t → ∞ is studied.