SINGLE-POINT CONDENSATION AND LEAST-ENERGY SOLUTIONS

We prove a conjecture raised in our earlier paper which says that the least-energy solutions to a two-dimensional semilinear problem exhibit single-point condensation phenomena as the nonlinear exponent gets la rge. Our method is based on a sharp form of a well-known borderline ca se of the Sobolev embedding theory. With the help of this embedding, w e can use the Moser iteration scheme to carefully estimate the upper b ound of the solutions. We can also determine the location of the conde nsation points.