The Polynomial Function Model in Born-Infeld Theory

DAI Bing-bing, ZHANG Rui-feng

doi:10.13371/j.cnki.chin.q.j.m.2022.03.001

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 3: 221 - 236

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.03.001

The Polynomial Function Model in Born-Infeld Theory

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School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

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.

Received date: 2022-08-31

Online published: 2022-09-19

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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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

Cite this article

DAI Bing-bing, ZHANG Rui-feng . The Polynomial Function Model in Born-Infeld Theory[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(3) : 221 -236 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.001

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