POSITIVE SOLUTIONS FOR p-LAPLACIAN EQUATIONS WITH CONCAVE TERMS

We consider a nonlinear Dirichlet problem driven by the p-Laplacian differential operator, with a nonlinearity concave near the origin and a nonlinear perturbation of it. We look for multiple positive solutions. We consider two distinct cases. One when the perturbation is p-linear and resonant with respect to lambda(1) > 0 (the principal eigenvalue of (-Delta(p), W-0(1,p)(Z))) at infinity and the other when the perturbation is p-superlinear at infinity. In both cases we obtain two positive smooth solutions. The approach is variational, coupled with the method of upper-lower solutions and with suitable truncation techniques.