Existence results are established for a second order boundary value problem on the half line motivated from the model of a slender dry patch in a liquid film draining under gravity down an inclined plane.
"INFINITE INTERVAL PROBLEMS ARISING IN THE MODEL OF A SLENDER DRY PATCH IN A LIQUID FILM DRAINING UNDER GRAVITY DOWN AN INCLINED PLANE." Methods Appl. Anal. 10 (3) 363 - 376, Sept 2003.