Concentration phenomena in elliptic problems with critical and supercritical growth

This paper deals with the existence of positive solutions of problem -∆u = u N +2 N -2 + εw(x)u q , with Dirichlet zero boundary condition on Ω (a bounded domain in R N ), when q ≥ 1 and q = N +2 N -2 .We study the existence of solutions which blow-up and concentrate at a single point of Ω whose location depends on the Robin function and on the coefficient w of the perturbed term.Definition 1.1.Let u ε be a family of solutions for (1.1).We say that u ε blow-up and concentrate at a point ξ 0 if there exist rates of concentration