THE EXISTENCE AND NON-EXISTENCE OF CONVEX- OR CONVEX-CONCAVE SOLUTIONS OF A DIFFERENTIAL EQUATION RESULTING FROM FLUID MECHANICS

A similar problem was recently considered with f' (t) -> lambda as t -> T-c, is the maximum value for the existence or no existence of f(c)), lambda is an element of 0, 1, +/-infinity} and 0 < beta < 1. In this paper, we study same the equation (with beta < 0) and we establish the existence of solutions satisfying the boundary conditions f (0) = a is an element of R, f'(0) = b < 0 and f'(+infinity) is an element of {0,1}. In order to do that, we utilize the shooting technique, then we consider the initial value problem consisting of the differential equation such that f '' (0) = a is an element of R, f' (0) = b < 0 and f ''(0) = c >= 0. We accompany our results by some numerical illustrations.