A Dirichelet-Neumann m-point BVP with a p-Laplacian-like operator

Let φ, θ be odd increasing homeomorphisms from R onto R satisfying φ(0)=θ(0)=0, and let f:[a,b]×R×R→R be a function satisfying Carathe´odory's conditions. Let αi∈R, ξi∈(a,b), i=1,…,m-2, a<ξ1<ξ2<⋯<ξm-21 or ∑i=1m-2αi<1.