Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval

We use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional p-Laplacian u′t|p−2u′t′+λfut=0, t∈0,1, u(0)=u(1)=0, where p∈(1,2], λ∈(0,∞) is a parameter, f∈C1([0,r),[0,∞)) for some constant r>0, f(s)>0 in (0,r), and lims→r-(r-s)p-1f(s)=+∞.