A new proof on quasilinear Schrödinger equations with prescribed mass and combined nonlinearities

2025/09/14 by Jianhua Chen, Chen, Jianhua, Jijiang Sun +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2509.11073

openalex publication_date 2025/09/14 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/30

Abstract

In this work, we study the quasilinear Schrödinger equation \aligned -Δu-Δ(u²)u=|u|^p-2u+|u|^q-2u+λu, x∈\R^N, \endaligned under the mass constraint ∫_\R^N|u|²dx=a, where N≥2, 20 is a given mass and λ is a Lagrange multiplier. As a continuation of our previous work (Chen et al., 2025, arXiv:2506.07346v1), we establish some results by means of a suitable change of variables as follows: \beginitemize \item[\bf(i) ] \bf qualitative analysis of the constrained minimization For 20; \enditemize \beginitemize \item[\bf(ii)]\bf existence of two radial distinct normalized solutions For 2

Citations

• Existence and multiplicity of normalized solutions for the quasi-linear Schrödinger equations with mixed nonlinearities
• Normalized solutions for a Sobolev critical quasilinear Schrödinger equation
• Another look at quasilinear Schrödinger equations with prescribed mass via dual method
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• Normalized solutions of L²-supercritical NLS equations on compact metric graphs
• Orbital stability of ground states for a Sobolev critical Schrödinger equation
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• Multiple normalized solutions for quasi-linear Schrödinger equations
• Stability and instability results for standing waves of quasi-linear Schrödinger equations
• The existence of surfaces of constant mean curvature with free boundaries
• Nonlinear Schr�dinger equations and sharp interpolation estimates

Related

• Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity
• Another look at quasilinear Schrödinger equations with prescribed mass via dual method
• Existence and multiplicity of normalized solutions for the quasi-linear Schrödinger equations with mixed nonlinearities
• Nonradial normalized solutions for a quasilinear Schrödinger equation via dual approach
• Quasilinear Schrödinger equations with concave and convex nonlinearities