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On the dynamics of the generalized Emden-Fowler equation. (English) Zbl 0961.34021
The authors present some new results dealing with the qualitative behavior of solutions to the quasilinear second-order differential equation $[a(t)\Phi_p(x'(t))]'-b(t)\Phi_q(x(t))=0 \tag{1}$ where $$a,\;b$$ are positive continuous real functions, and $$\Phi_j(u)=|u|^{j-2}u$$, $$j>1$$. Here, all solutions to (1) are divided with respect to their asymptotic behavior into two classes. In addition, some asymptotic estimates are presented and the convergence of solutions to zero as $$t\to\infty$$ is studied. A topological approach is employed and a fixed-point result is used in the work.

##### MSC:
 34C11 Growth and boundedness of solutions to ordinary differential equations
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