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Research Article | Open Access

Symmetry breaking for a Schrödinger equation with van der Waals type potentials

Na Huang( ), Yumi Shao, Hongmin Suo
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
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Abstract

We study the asymptotic behavior of ground state energy for a Schrödinger equation with van der Waals type potentials. We prove that when the mass c is sufficiently large, the ground state energy restricted to radially symmetric functions is greater than the ground state energy. This result implies that the symmetry of the ground state solution of the equation is broken.

Keywords

Schrödinger equationsvan der Waals type potentialssymmetry breaking
CLC number: 35B09, 35J20, 35Q40, 35Q55

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AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 13805-13817
DOI: 10.3934/math.2026568

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Cite this article:
Huang N, Shao Y, Suo H. Symmetry breaking for a Schrödinger equation with van der Waals type potentials. AIMS Mathematics, 2026, 11(5): 13805-13817. https://doi.org/10.3934/math.2026568

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Received: 09 March 2026
Revised: 16 April 2026
Accepted: 22 April 2026
Published: 15 May 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)