On a singular minimizing problem

We investigate the non-homogeneous modular Dirichlet problem Δ _p (·)u(x) = f (x) (where Δ _p (·)u(x) = div(|?u|^p(x-2)?u(x)) from the functional analytic point of view and we prove the stability of the solutions ({left( {{u_{{p_i}}}} right)_i}) of the equation ({Delta _{{p_i}left( cdot right)}}{u_{{p_i}left( cdot right)}} = f) as p _i (·) → q(·) via Gamma-convergence of sequence of appropriate functionals.