**M. Cecchi, Z. Dosla, M. Marini**

## On the dynamics of the generalized Emden-Fowler equation

**abstract:**

We present some recent results dealing with the qualitative behavior
of solutions of the quasilinear second order differential equation
% (*)
\begin{equation}
\big[a(t)\Phi_p(x^{^{\prime}})\big]^{^{\prime}}-b(t)\Phi_q(x)=0
\tag{$*$}
\end{equation}
where $a$, $b$ are positive continuous real functions,
and $\Phi_{j}(u)=|u|^{j-2}u$, $j>1$.
Following a classification of solutions, proposed in the linear case
in [3], 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 $t\to\infty$ is studied.