带混合排异非线性项的薛定谔方程基态的极限性质——献给李工宝教授 70 寿辰

Abstract

Abstract:

JeanJean-Lu obtained the existence of ground states for the Schrödinger equation with mixed-type nonlinearities in the reference [Calc Var Partial Differential Equations, 2022]. Based on this fact, by analyzing the quantitative relationship between energy, frequency and mass, we prove that under appropriate rescalings, the ground state obtained in [Calc Var Partial Differential Equations, 2022] converges to the ground state of the classical Schrödinger equation with a single nonlinear term (when the mass declines) or converges to the ground state of the corresponding Thomas Fermi equation (when the mass tends to infinity). In particular, our conclusion holds true for the cubic-quintic nonlinear Schrödinger equation.

Key words: Schr?dinger equation, mixed repulsive terms, ground state, limiting property.

CLC Number:

O175.23

Xiao Luo, Xi Qin. Limiting Properties of Ground States for the Schrödinger Equation with Mixed Repulsive Nonlinear Terms[J].Acta mathematica scientia,Series A, 2025, 45(6): 1942-1960.

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References 20

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Limiting Properties of Ground States for the Schrödinger Equation with Mixed Repulsive Nonlinear Terms

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