一类带有吸引库伦势的 Schrödinger 方程正规化解的多重性——献给邓引斌教授 70 寿辰

Abstract

Abstract:

In this paper, we focus on the solutions to the Schrödinger equation with attractive Coulomb potential

$-\Delta u -|x|^{-1}u-|u|^{p-2}u-\lambda u=0,\,\,\,\,\ x\in\mathbb{R}^3,$

under the normalized constriant

$\int_{\mathbb{R}^3} u^2(x){\rm d}x=c$

where $p\in(\frac{10}{3},6), \lambda\in\mathbb{R}$. We show that for small mass, the ground states exist and correspond to local minima of the associated energy functional. The existence of the excited states is also obtained. We next prove that the excited states are located at a mountain-pass level of energy functional. Finally, the existence of infinitely many high energy solutions is established by using a minimax procedure.

Key words: Schr?dinger equation, coulomb potential, normalized solutions

CLC Number:

O175.23

Lu Lu. Multiple of Normalized Solutions of a Class of Schrödinger Equations with Attractive Coulomb Potential[J].Acta mathematica scientia,Series A, 2026, 46(4): 1344-1359.

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References 20

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Multiple of Normalized Solutions of a Class of Schrödinger Equations with Attractive Coulomb Potential

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