Multiplicity results for a class of gradient systems depending on two parameters

In this paper we prove the existence of at least three solutions for a class of two-point boundary value systems of the type {−ui″+ui=λFui(x,u1,…,un)+μGui(x,u1,…,un),ui′(a)=ui′(b)=0 for 1≤i≤n1≤i≤n. The approach is fully based on a recent three critical points theorem of Ricceri [B. Ricceri, A three critical points theorem revisited, Nonlinear Anal., 70 (9) (2009) 3084–3089].