We study asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations. All solutions are classified into six types by means of their asymptotic behavior. Necessary and/or sufficient conditions are given for such equations to possess a solution of each of the six types.

First order neutral di¤erential equations are studied and sufficient conditions are derived for every solution to be oscillatory. Our approach is to reduce the oscillation of neutral differential equations to the nonexistence of eventually positive solutions of non-neutral differential inequalities. Our results extend and improve several known results in the literature.

Standing pulse solutions of three-component systems with competition and diffusion are considered. Under the assumption that travelling front and back solutions with the same zero velocity coexist, it is shown that standing pulse solutions bifurcate globally from these travelling front and back solutions. The direction of bifurcation and stability properties of bifurcated solutions are also shown.

We investigate generalized solutions of nonlinear diffusion equations in the sense of Colombeau and extend the results of Biagioni and Oberguggenberger [2] to more general equations. We prove the existence and uniqueness of a generalized solution which is shown to be consistent with the classical solution.