Asymptotics of solutions for a class of quasilinear second-order ordinary differential equations

We consider a class of quasilinear second-order ordinary differential equations that arise in the investigation of the problem on stationary convective mass transfer between a drop and a solid medium in the presence of a volume chemical reaction of power-law form [F(υ) ≡ υν] for the case in which the Peclet number Pe and the rate constant kυ of the volume chemical reaction tend to infinity. We prove the existence and uniqueness theorem for a boundary value problem and analyze asymptotic properties of the solution.