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

Na Huang; Yumi Shao; Hongmin Suo; Na Huang; Yumi Shao; Hongmin Suo

doi:10.3934/math.2026568

AIMS Mathematics

2026, Volume 11, Issue 5: 13805-13817. doi: 10.3934/math.2026568

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Research article

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

School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

Received: 09 March 2026 Revised: 16 April 2026 Accepted: 22 April 2026 Published: 18 May 2026
MSC : 35B09, 35J20, 35Q40, 35Q55

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.
- Schrödinger equations,
- van der Waals type potentials,
- symmetry breaking
Citation: Na Huang, Yumi Shao, Hongmin Suo. Symmetry breaking for a Schrödinger equation with van der Waals type potentials[J]. AIMS Mathematics, 2026, 11(5): 13805-13817. doi: 10.3934/math.2026568

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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.

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