Existence and multiplicity of normalized solutions for the quasi-linear Schrödinger equations with mixed nonlinearities

2025/07/01 by He, Qihan, Wang, Hao · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.00375

Abstract

In this paper, we study the existence and multiplicity of the normalized solutions to the following quasi-linear problem -Δu-Δ(|u|²)u+λu=|u|^p-2u+τ|u|^q-2u, in ℝ^N,~ 1≤ N≤4, with prescribed mass ∫_ℝ^N|u|²dx=a , where λ∈ℝ appears as a Lagrange multiplier and the parameters a,τ are all positive constants. We are concerned about the mass-mixed case 2

Citations

• Serrin-type Overdetermination in Scaling Limits: Sharp Existence and Asymptotic Behavior of Quasi-linear Schrödinger Energy Ground States
• Standing wave solutions of a quasilinear Schrödinger equation in the small frequency limit
• Existence and multiplicity of sign-changing solutions for quasilinear Schrödinger equations with sub-cubic nonlinearity
• Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case
• Multiple normalized solutions for quasi-linear Schrödinger equations
• Stability and instability results for standing waves of quasi-linear Schrödinger equations
• Nonlinear scalar field equations, I existence of a ground state

Cited by

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

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