Existence and uniqueness for a class of quasilinear elliptic boundary value problems

We prove existence and uniqueness of positive solutions for the boundary value problem (rN−1φ(u′))′=−λrN−1f(u), u′(0)=u(1)=0,where φ(x)=xp−2x, f(x)/xp−1 may not be decreasing on (0,∞), and λ is a large parameter.