Multi‐bumps solutions for the nonlinear Schrödinger equation under a slowing decaying potential

Abstract

In this paper, we consider the following nonlinear Schrödinger equation: where , and have the algebraical decay that as , where , and . By introducing the Miranda theorem, via the Lyapunov–Schmidt finite‐dimensional reduction method, we construct infinitely many multi‐bumps solutions of (0.1), whose maximum points of bumps lie on the top and bottom circles of a cylinder provided , or . This result complements and extends the ones in [Duan and Musso, JDE, 2022] for a slow decaying rate of the potential function at infinity from to .