Pohozaev manifold constraint for solving nonlinear Schr\"odinger equations with potentials vanishing at infinity

Existence of a positive solution for a class of nonlinear Schr"odinger equations with potentials which decay to zero at infinity, with an appropriate rate, approaching zero mass type limit scalar field equations, is established via a new composition of two translated and dilated solitons and its projection on the so called Pohozaev manifold.