Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

Consideration is given to a class of nonlinear third-order differential equations arising in fluid flow over a nonlinearly stretching sheet. Existence of a solution of the nonlinear third-order differential equation over 0<η<∞ is established in this paper, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609–618). That is, we prove with estimates independent of R for solutions of the third-order differential equation on [0, R]. The existence of a solution on 0<η<∞ follows from the Ascoli–Arzela Theorem. Furthermore, numerical solutions are obtained and presented through graphs, and the influence of the physical parameter on the flow characteristics is discussed.