Uniqueness results for the one-dimensional p-Laplacian

This paper is concerned with positive solutions of the boundary value problem (|y′|p−2y′)′+f(y)=0, y(−b)=0=y(b) where p>1, b is a positive parameter. Assume that f is continuous on (0,+∞), changes sign from nonpositive to positive, and f(y)/yp−1 is nondecreasing in the interval of f>0. The uniqueness results are proved using a time-mapping analysis.