Affiliation:
1. College of Mathematics and Computing Science Hunan University of Science and Technology Xiangtan Hunan China
2. Department of Mathematics and Finance Hunan University of Humanities, Science and Technology Loudi Hunan China
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
.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Hunan Province
Subject
General Engineering,General Mathematics