On the location of concentration points for singularly perturbed elliptic equations

By exploiting a variational identity of Pohozaev-Pucci-Serrin\r\ntype for solutions of class C1, we get some necessary conditions for\r\nlocating the peak-points of a class of singularly perturbed quasilinear\r\nelliptic problems in divergence form. More precisely, we show that the\r\npoints where the concentration occurs, in general, must belong to what\r\nwe call the set of weak-concentration points. Finally, in the semilinear\r\ncase, we provide a new necessary condition which involves the Clarke\r\nsubdifferential of the ground-state function.