Positive decreasing solutions of second order quasilinear ordinary differential equations in the framework of regular variation

Jelena Milošević, Jelena V. Manojlović

This paper is concerned with asymptotic analysis of positive decreasing solutions of the secondorder quasilinear ordinary differential equation \begin{equation}ag{E} (p(t)ǎrphi(|x'(t)|))'=q(t)si(x(t)), \end{equation} with the regularly varying coefficients $p$, $q$, $\varphi$, $\psi$. An application of the theory of regular variation gives the possibility of determining the precise information about asymptotic behavior at infinity of solutions of equation (E) such that $\lim\limits_{t\to\infty}x(t)=0$, $\lim\limits_{t\to\infty}p(t)\varphi(-x'(t))=\infty$.