Multiple Normalized Solutions to a Class of Modified Quasilinear Schrodinger Equations Schrodinger Equations (2411.15962v1)

Abstract: We investigate the existence, non-existence, and multiplicity of positive solutions to a class of quasilinear Schrodinger equations with a prescribed mass condition in higher dimensions. Using the dual approach, the equation is transformed into a corresponding semilinear form. A global branch approach is employed to address nonlinearities that may be mass subcritical, critical, or supercritical. This study further examines the asymptotic behavior of positive solutions as the parameter approaches zero or infinity and identifies a continuum of unbounded solutions within the functional space under consideration.