Positive multi-bump solutions for the Schrödinger equation with slow decaying competing potentials

We are concerned with the existence of multi-bump solutions to the following nonlinear Schrödinger equation with competing potentials V and Q,−Δu+V(|x|)u=Q(|x|)up,u>0inRN, where N≥3,10. By introducing a weighted norm and some delicate analysis, we construct infinitely many new positive multi-bump solutions for m1 to the slow decaying potentials case m,n>0.