Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Carathéodory terms. One is parametric, (p-1)-sublinear with a partially concave nonlinearity near zero. The other is (p- 1) -superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter λ> 0 varies.