Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres

We study positive bound states for the equation. -ε2δu+V(x)u=K(x)f(u),x∈RN, where ε > 0 is a real parameter and V and K are radial positive potentials. We are especially interested in solutions which concentrate on a k-dimensional sphere, 1 ≤ k≤. N- 1, as ε → 0. We adopt a purely variational approach which allows us to consider broader classes of potentials than those treated in previous works. For example, V and K might be singular at the origin or vanish superquadratically at infinity. © 2011 Elsevier Inc.SCOPUS: ar.j