Multiple Normalized Solutions to a Class of Modified Quasilinear Schrödinger Equations

Abstract

In our research, we focus on the existence, non-existence, and multiplicity of positive solutions to a Quasilinear Schrödinger equation with prescribed mass. The dual approach is used to transform this equation into a corresponding semi-linear form. Then, we implement a global branch approach, adeptly handling nonlinearities  that fall into mass subcritical, critical, or supercritical categories. Key aspects of this study include examining the positive solutions' asymptotic behaviors and identifying a continuum of unbounded solutions.