Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex nonlinearities

We consider a nonlinear parametric Dirichlet equation driven by a nonhomogeneous differential operator involving a reaction exhibiting the competing effects of concave and convex terms. Using variational methods combined with truncation and comparison techniques we prove a bifurcation near zero theorem describing the dependence of the positive solutions on the parameter (lambda >0).