A singular elliptic equation and a related functional

We study a class of Dirichlet boundary value problems whose prototype is where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p-2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non-differentiable functional on whose formal Euler-Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.