The role of interplay between coefficients in the $G$-convergence of some elliptic equations

We study the behavior of the solutions $u$ of the linear Dirichlet problems $-\mathrm{d}\mathrm{i}\mathrm{v}(M(x)\mathrm{\nabla }u)+a(x)u=f(x)$ with respect to perturbations of the matrix $M(x)$ (with respect to the $G$-convergence) and with respect to perturbations of the nonnegative coefficient $a(x)$ and of the right hand side $f(x)$ satisfying the condition $\mathrm{\mid }f(x)\mathrm{\mid }\le Qa(x)$.