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 �-Laplacian operator and posed on the positive half-line: � (�(-x 00 )) 0 (t) + f(t,x(t)) = 0, t > 0, x(0) = µx 0 (0), x 0 (+1) = x 00 (+1) = 0 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.