Multiple Normalized Solutions to a Class of Modified Quasilinear Schrodinger Equations Schrodinger Equations

TL;DR

This paper explores the existence, multiplicity, and behavior of positive solutions to a class of modified quasilinear Schrödinger equations, employing dual and global branch methods to analyze solutions across different regimes and parameter limits.

Contribution

It introduces a novel approach combining dual transformation and global branch techniques to study solutions of modified quasilinear Schrödinger equations with various nonlinearities.

Findings

Existence and multiplicity of positive solutions established.

Asymptotic behavior of solutions analyzed as parameters vary.

Identified a continuum of unbounded solutions in the functional space.

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.