Asymptotic analysis of positive solutions of third order nonlinear differential equations

Abstract

It is shown that an application of the theory of regular variation (in the sense of Karamata) gives the possibility of determining the existence and precise asymptotic behavior of positive solutions of the third-order nonlinear differential equation $(|x''|^{\alpha-1}x'')' + q(t)|x|^\beta x = 0$, where $\alpha > \beta > 0$ are constants and $q:[a,\infty)\to(0,\infty)$ is a continuous regularly varying function.