数学季刊 ›› 2022, Vol. 37 ›› Issue (3): 221-236.doi: 10.13371/j.cnki.chin.q.j.m.2022.03.001

• •    下一篇

Born-Infeld理论中的多项式函数模型

  

  1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
  • 收稿日期:2022-08-31 出版日期:2022-09-25 发布日期:2022-09-19
  • 通讯作者: ZHANG Rui-feng (1964-), female, native of Kaifeng, Henan, professor of Henan University, Ph.D supervisor, Ph.D, engages in partial differential equation. E-mail:zrf615@henu.edu.cn
  • 作者简介: DAI Bing-bing (1992-), female, native of Zhumadian, Henan, graduate student of Henan University, engages in partial differential equation; ZHANG Rui-feng (1964-), female, native of Kaifeng, Henan, professor of Henan University, Ph.D supervisor, Ph.D, engages in partial differential equation.
  • 基金资助:
    Supported by National Natural Science Foundation of He’nan Province of China (Grant
    No. 222300420416); National Natural Science Foundation of China (Grant Nos. 11471099, 11971148); Graduate
    Talents Program of Henan University (Grant No. SYLYC2022078).

The Polynomial Function Model in Born-Infeld Theory

  1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
  • Received:2022-08-31 Online:2022-09-25 Published:2022-09-19
  • Contact: ZHANG Rui-feng (1964-), female, native of Kaifeng, Henan, professor of Henan University, Ph.D supervisor, Ph.D, engages in partial differential equation. E-mail:zrf615@henu.edu.cn
  • About author: DAI Bing-bing (1992-), female, native of Zhumadian, Henan, graduate student of Henan University, engages in partial differential equation; ZHANG Rui-feng (1964-), female, native of Kaifeng, Henan, professor of Henan University, Ph.D supervisor, Ph.D, engages in partial differential equation.
  • Supported by:
    Supported by National Natural Science Foundation of He’nan Province of China (Grant
    No. 222300420416); National Natural Science Foundation of China (Grant Nos. 11471099, 11971148); Graduate
    Talents Program of Henan University (Grant No. SYLYC2022078).

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摘要：  Based on the Lagrangian action density under Born-Infeld type dynamics and
motivated by the one-dimensional prescribed mean curvature equation, we investigate the
polynomial function model in Born-Infeld theory in this paper with the form of
−([1−a(ϕ')2 ]ϕ' )' =λf(ϕ(x)),
where λ> 0 is a real parameter, f ∈C2 (0 , + ∞ ) is a nonlinear function. We are interested
in the exact number of positive solutions of the above nonlinear equation. We specifically
develop for the problem combined with a careful analysis of a time-map method.

关键词:  Time-map analysis, Exact number of solutions, Lagrangian action density, The polynomial function model, Born-Infeld theory

Abstract:  Based on the Lagrangian action density under Born-Infeld type dynamics and
motivated by the one-dimensional prescribed mean curvature equation, we investigate the
polynomial function model in Born-Infeld theory in this paper with the form of
−([1−a(ϕ')2 ]ϕ' )' =λf(ϕ(x)),
where λ> 0 is a real parameter, f ∈C2 (0 , + ∞ ) is a nonlinear function. We are interested
in the exact number of positive solutions of the above nonlinear equation. We specifically
develop for the problem combined with a careful analysis of a time-map method.

Key words:  Time-map analysis, Exact number of solutions, Lagrangian action density; The polynomial function model, Born-Infeld theory

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