Summary: This paper deals with the existence of positive solutions of problem \(-\Delta u=u^{N+2\over N-2}+{\varepsilon} w(x)u^q\), with Dirichlet zero boundary condition on \(\Omega\) (a bounded domain in \(\mathbb R^N\)), when \(q\geq 1\) and \(q\neq{N+2\over N-2}\). We study the existence of solutions which blow-up and concentrate at a single point of \(\Omega\) whose location depends on the Robin function and on the coefficient \(w\) of the perturbed term.