Abstract: The author considered  the existence of positive solutions for the mixed boundary value problems of the onedimensional p-Laplacian equations  with nonlinearities changing signs, by using the nowhere normaloutward compact map’s fixed point index theorem, under the condition of f(t,0)≥0 and p-sublinear conditions, the author obtained the existence of the positive solution of the problem.

Key words: p-Laplacian equation, positive solution, nowhere normaloutward map, fixed point index