Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials

We establish the existence and multiplicity of semiclassical bound states of the following nonlinear Schrödinger equation:{−ε2Δu+V(x)u=g(x,u)for x∈RN,u(x)→0as |x|→∞ where V changes sign and g   is superlinear with critical or supercritical growth as |u|→∞|u|→∞.