Previous Article in Journal
A Study of the (a,b)-Deformed Free Convolution
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Symmetry
Volume 17
Issue 11
10.3390/sym17111955
symmetry-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Sign-Changing Solutions to the Schrödinger Equations Coupled with a Neutral Scalar Field

by
Xiao-Qi Liu
1,*,
Hongwei Wang
1,
Qinglei Hui
1 and
Li-Feng Yin
2
1
School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China
2
School of Statistics and Mathematics, Sichuan Normal University, Chengdu 610039, China
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(11), 1955; https://doi.org/10.3390/sym17111955 (registering DOI)
Submission received: 11 October 2025 / Revised: 7 November 2025 / Accepted: 10 November 2025 / Published: 13 November 2025
(This article belongs to the Section Mathematics)
Versions Notes

Abstract

Here we consider the problem of the Schrödinger equation coupled with a neutral scalar field. Through the methods of descending flow invariant sets via the Ljusternik–Schnirelman theory, we rigorously demonstrate the existence of infinitely many sign-changing solutions.
Keywords: variational method; critical point theory; infinitely many sign-changing solutions; invariant sets; descending flow variational method; critical point theory; infinitely many sign-changing solutions; invariant sets; descending flow

Share and Cite

MDPI and ACS Style

Liu, X.-Q.; Wang, H.; Hui, Q.; Yin, L.-F. Sign-Changing Solutions to the Schrödinger Equations Coupled with a Neutral Scalar Field. Symmetry 2025, 17, 1955. https://doi.org/10.3390/sym17111955

AMA Style

Liu X-Q, Wang H, Hui Q, Yin L-F. Sign-Changing Solutions to the Schrödinger Equations Coupled with a Neutral Scalar Field. Symmetry. 2025; 17(11):1955. https://doi.org/10.3390/sym17111955

Chicago/Turabian Style

Liu, Xiao-Qi, Hongwei Wang, Qinglei Hui, and Li-Feng Yin. 2025. "Sign-Changing Solutions to the Schrödinger Equations Coupled with a Neutral Scalar Field" Symmetry 17, no. 11: 1955. https://doi.org/10.3390/sym17111955

APA Style

Liu, X.-Q., Wang, H., Hui, Q., & Yin, L.-F. (2025). Sign-Changing Solutions to the Schrödinger Equations Coupled with a Neutral Scalar Field. Symmetry, 17(11), 1955. https://doi.org/10.3390/sym17111955

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop