Multi-bump solutions for a Schrödinger equation with prescribed L2-norm via a fixed point approach

This paper focuses on investigating the existence of multi-bump solutions for the following non-homogeneous Schrödinger equation with prescribed [Formula: see text]-norm in [Formula: see text] [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are viewed as a potential functions, [Formula: see text] belongs to the dual of our working space and the f is considered a continuous function that satisfies exponential critical growth when [Formula: see text] and subcritical growth when [Formula: see text]. We consider that function [Formula: see text] has a potential well [Formula: see text] consisting of k isolated connected components. Instead of using variational methods, we adopt a modified fixed point theorem to investigate the problem. Specifically, for [Formula: see text] sufficiently large, this approach establishes the existence of at least [Formula: see text] multi-bump positive solutions for the above equation.