Consider a sequence of uniformly elliptic symmetric operators \(A_{\epsilon}: H^ 1_ 0(\Omega)\to H^{-1}(\Omega)\) of the form \(A_{\epsilon}=-\sum^{n}_{i,j=1}D_ i(a^{\epsilon}_{ij}(x)D_ j)\) and assume that \(A_{\epsilon}\) G-converges to \(A_ 0\) in the sense that \(A_{\epsilon}^{-1}f\) converges to \(A_ 0^{-1}f\) weakly in \(H^ 1_ 0(\Omega)\) for every \(f\in H^{-1}(\Omega)\). Given \(h\in L^ 2(\Omega)\) and a continuous function \(g: {\mathbb{R}}\to {\mathbb{R}}\), do the solutions of \(A_{\epsilon}u=g(u)+h\) converge weakly in \(H^ 1_ 0(\Omega)\) to the solutions of \(A_ 0u=g(u)+h ?\) In the present paper the problem above is studied under the following assumption: \(i)\quad \lim_{s\to \pm \infty}g(s)/s=k_{\pm}\in {\mathbb{R}};\) ii) \([k_-,k_+]\cap Sp(A_ 0)=\{k\}\) where \(Sp(A_ 0)\) is the spectrum of \(A_ 0\) and k is a simple eigenvalue of \(A_ 0\); iii) g is strictly convex.