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.


34C11 Growth and boundedness of solutions to ordinary differential equations
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