Exact multiplicity results for a class of two-point boundary value problems

This paper is concerned with the exact number of positive solutions for boundary value problems ′(|y′|p−2y′)+λf(y)=0 and y(−1)=y(1)=0, where p>1 and λ>0 is a positive parameter. We consider the case in which the nonlinearity f is positive on (0,∞) and (p−1)f(u)−uf′(u) changes sign from negative to positive.