Characterization of slowly decaying positive solutions of second-order quasilinear ordinary differential equations with sub-homogeneity

摘要

We consider quasilinear ordinary differential equations with sub-homogeneity near infinity. A necessary and sufficient condition is obtained for the equations to have slowly decaying positive solutions. Asymptotic forms of such positive solutions are established. As an application of these results, we obtain Liouville-type theorems for quasilinear elliptic problems.