SINGULAR EQUATIONS WITH VARIABLE EXPONENTS AND CONCAVE-CONVEX NONLINEARITIES

We consider a nonlinear anisotropic Dirichlet problem with a reaction that has the combined effects of three distinct nonlinearities: a parametric singular term, a parametric "concave" term (the parameter lambda > 0 is the same in both) and a nonparametric "convex" perturbation. So, the problem is a singular version of the well known "concave-convex" problem. We prove an existence and multiplicity result which is global in the parameter lambda > 0 (a bifurcation-type theorem). We also indicate some small improvements in the case of (p(z), q(z)) and p(z )-equations.