Upper and lower solutions for φ−Laplacian third-order BVPs on the half-Line

Abstract

In this paper, we investigate the existence of positive solution for a class of singular third-order boundary value problem associated with a φ-Laplacian operator and posed on the positive half-line:

                                                               

where µ ≥ 0. By using the upper and lower solution approach and the fixed point theory, the existence of positive solutions is proved under a monotonic condition on f. The nonlinearity f may be singular at x = 0. An example of application is included to illustrate the main existence result.