Multiple positive solutions for nonautonomous quasicritical elliptic problems in unbounded domains

The problem -Delta u + a(epsilon)(x)u = u(N+2/N-2-epsilon), epsilon > 0, with boundary Dirichlet zero data is considered in an exterior domain Omega subset of R-N Assuming that, as epsilon -> 0, a(epsilon) concentrates and blows up at a point of Omega, namely a(epsilon)(x) = a(0) + 1/(epsilon)2aa (x-x(0/)epsilon(a))alpha is an element of R+\{0}, x(0) is an element of Omega, the existence of at least 2 distinct positive solutions is proved, if vertical bar a vertical bar(LN/2) is suitably small. Furthermore, if a(epsilon) (x) has a Suitable behaviour at infinity, the existence of another positive solution is shown.