Two positive solutions for second-order quasilinear differential equation boundary value problems with sign changing nonlinearities

In this paper, the second order quasilinear differential equation (Φ(y′))′+q(t)f(t,y)=0, 0<t<1 subject to Dirichlet boundary conditions and mixed boundary conditions is studied, where f is allowed to change sign, Φ(v)=|v|p−2v, p>1. We show the existence of at least two positive solutions by using a new fixed point theorem in cones.