Normalized solutions of quasilinear Schrödinger equation with Sobolev critical exponent on star-shaped bounded domains

2025/09/16 by Yan Ru, Yan, Ru
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.12707

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a quasilinear Schrödinger equation with critical exponent on bounded domains. Via a dual approach, we establish the existence of two positive normalized solutions: one is a ground state and the other is a mountain pass solution.

Citations

• Normalized solutions for a Sobolev critical quasilinear Schrödinger equation
• Positive normalized solutions of Schrödinger equations with Sobolev critical growth in bounded domains
• Two Positive Normalized Solutions on Star-shaped Bounded Domains to the Brézis-Nirenberg Problem, I: Existence
• Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity
• Infinitely many normalized solutions for a quasilinear Schrodinger equation
• Normalized concentrating solutions to nonlinear elliptic problems
• Normalized bound states for the nonlinear Schrodinger equation in\n bounded domains
• A natural constraint approach to normalized solutions of nonlinear\n Schr "odinger equations and systems
• A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems
• Multiple normalized solutions for quasi-linear Schrödinger equations

Related

• Normalized solutions for a Sobolev critical quasilinear Schrödinger equation
• Ground state and multiple normalized solutions of quasilinear Schrödinger equations in the L²-supercritical case and the Sobolev critical case
• Normalized solutions for Sobolev critical Schrödinger equations on bounded domains
• Existence and Multiplicity of Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains
• Normalized solutions for some quasilinear elliptic equation with critical Sobolev exponent