Multiple solutions for quasilinear elliptic problems with concave and convex nonlinearities

We prove the existence of multiple signed bounded solutions for a quasilinear elliptic equation with concave and convex nonlinearities. For this, we use a variational approach in an intersection Banach space indroduced by Candela and Palmieri, and a truncation technique given by Garcia Azorero and Peral.