The authors consider the nonlinear boundary value problem
where , are continuous.
By using the upper and lower solutions method, the authors present sufficient conditions for the existence of solutions to (1).
Note: The authors point out that no other works on boundary value problems on the half-line for third-order differential equation by the other researchers have been considered by them as a prototyp. Such problem has been considered, for example, in the work of A. I. Kolosov and S. V. Kolosova [On two-sided approximations in the solution of the Falkner-Skan problem. Mat. Fiz. 23, 63–67 (1978; Zbl 0447.34014)].