Positive solutions for nonlinear periodic problems with concave terms

We consider a nonlinear periodic problem, driven by the scalar p-Laplacian, with a parametric concave term and a Carathéodory perturbation whose potential (primitive) exhibits a p-superlinear growth near +∞, without satisfying the usual in such cases Ambrosetti–Rabinowitz condition. Using critical point theory and truncation techniques, we prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies.