We study the Dirichlet boundary value problem for the p-Laplacian of the form −∆pu − λ1|u| p−2u = f in Ω, u = 0 on ∂Ω, where Ω ⊂ N is a bounded domain with smooth boundary ∂Ω, N ≥ 1, p > 1, f ∈ C(Ω) and λ1 > 0 is the first eigenvalue of ∆p. We study the geometry of the energy functional Ep(u) = 1⁄ p ∫ Ω |∇u| p − λ1⁄ p ∫ Ω |u| p − ∫ Ω fu and show the difference between the case 1 <p< 2 and the case p > 2. We also give the characterization of the right hand sides f for which the above Dirichlet problem is solvable and has multiple solutions.