Singular elliptic equations with (p(z), q(z))-growth

We consider a singular Dirichlet problem driven by a variable unbalanced growth differential operator and a singular reaction with an unbounded coefficient and an exponent η ∈ C(Ω ̄) η ∈ C ( Ω ¯ ) which is less than 1 only near ∂ Ω ∂ Ω . Using approximations, we show that the problem has a unique bounded solution.