一个新的全局分歧定理及其在核反应堆模型中的应用

陈瑞鹏

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一个新的全局分歧定理及其在核反应堆模型中的应用

更新时间：2026-10-28

- 一个新的全局分歧定理及其在核反应堆模型中的应用
- A New Global Bifurcation Theorem and Its Applications in Non-Cooperative Models of Nuclear Reactors
- 武汉大学学报自然科学英文版 2026年页码：1-7
- 作者机构：
  
  北方民族大学数学与信息科学学院，宁夏银川 750021
- 作者简介：
  
  CHEN Ruipeng, male, Ph. D., Lecturer, research direction: nonlinear differential equations and systems. E-mail: ruipengchen@126.com
- 基金信息：
  
  the Natural Science Foundation of Ningxia Hui Autonomous Region of China(2025AAC030060);the First-Class DisciplinesFoundation of Ningxia Hui Autonomous Region of China(NXYLXK2017B09)
- DOI：
  中图分类号： O175.8
- 收稿：2025-10-24，
  
  网络首发：2026-10-27，
- 稿件说明：
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陈瑞鹏.一个新的全局分歧定理及其在核反应堆模型中的应用[J].武汉大学学报自然科学英文版,

CHEN Ruipeng.A New Global Bifurcation Theorem and Its Applications in Non-Cooperative Models of Nuclear Reactors[J].Wuhan University Journal of Natural Sciences,
陈瑞鹏.一个新的全局分歧定理及其在核反应堆模型中的应用[J].武汉大学学报自然科学英文版, DOI：https://doi.org/10.1051/wujns/001.

CHEN Ruipeng.A New Global Bifurcation Theorem and Its Applications in Non-Cooperative Models of Nuclear Reactors[J].Wuhan University Journal of Natural Sciences, DOI：,https://doi.org/10.1051/wujns/XXXXXXXX001.

摘要

本文针对非线性Sturm-Liouville问题

</mo><mi>u</mi><mo stretchy="false">)</mo><mo>+</mo><mi>g</mi><mo stretchy="false">(</mo><mi>t</mi><mo>

</mo><mi>u</mi><mo>

</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>'</mi></mrow></msup><mo>

</mo><mi>γ</mi><mo stretchy="false">)</mo><mo>

</mo><mtext> </mtext><mi>t</mi><mo>∈</mo><mo stretchy="false">(</mo><mn mathvariant="normal">0

1</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>b</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mi>u</mi><mo stretchy="false">(</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">0</mn><mo>

</mo><mtext> </mtext><msub><mrow><mi>b</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>u</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">0</mn></mtd></mtr></mtable></mrow></mfenced></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156464&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156483&type=

62.93555450

9.45444489

建立了全局分歧定理，其中

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156484&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156450&type=

2.39888883

3.38666677

在

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156470&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156465&type=

1.97555566

2.68111110

处不是Fréchet可微的。该定理表明分歧现象在某些区间

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156466&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156485&type=

13.40555668

4.51555586

发生，且包含

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156486&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156451&type=

11.14777756

3.80999994

的无界连通分支

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156471&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156467&type=

3.95111132

4.09222221

位于

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156487&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156452&type=

27.65777779

4.79777765

之中。应用上述全局分歧定理，我们证明了对于任意参数

</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo><mo>

</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156488&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156472&type=

14.67555618

3.38666677

非合作核反应堆模型

</mo><mi>u</mi><mo stretchy="false">)</mo><mo>

</mo><mtext> </mtext><mi>t</mi><mo>∈</mo><mo stretchy="false">(</mo><mn mathvariant="normal">0

1</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mrow><mi>v</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>=</mo><mi>μ</mi><mi>u</mi><mo>

</mo><mtext> </mtext><mi>t</mi><mo>∈</mo><mo stretchy="false">(</mo><mn mathvariant="normal">0

1</mn><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></mfenced></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156498&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156489&type=

44.73222351

9.45444489

至少存在一个正解。

Abstract

In this work

we establish a version of the global bifurcation theorem for nonlinear Sturm-Liouville problem

</mo><mi>u</mi><mo stretchy="false">)</mo><mo>+</mo><mi>g</mi><mo stretchy="false">(</mo><mi>t</mi><mo>

</mo><mi>u</mi><mo>

</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>'</mi></mrow></msup><mo>

</mo><mi>γ</mi><mo stretchy="false">)</mo><mo>

</mo><mtext> </mtext><mi>t</mi><mo>∈</mo><mo stretchy="false">(</mo><mn mathvariant="normal">0

1</mn><mo stretchy="false">)</mo><mo>

</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>b</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mi>u</mi><mo stretchy="false">(</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>'</mi></mrow></msup><mo stretchy="false">(</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">0</mn><mo>

</mo></mtd></mtr></mtable></mrow></mfenced></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156446&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156459&type=

54.61000061

8.32555580

where

is not Fréchet differentiable at

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156460&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156420&type=

1.69333339

2.25777793

. We show that the bifurcation occurs from some intervals

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156447&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156436&type=

11.57111073

3.95111132

; the connected component

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156461&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156421&type=

3.38666677

3.52777815

containing

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156448&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156437&type=

9.59555531

3.24555564

is unbounded and lies in

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156462&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156422&type=

24.41222382

4.09222221

By applying the above theorem

we prove that the non-cooperative model

</mo><mi>u</mi><mo stretchy="false">)</mo><mo>

</mo><mtext> </mtext><mi>t</mi><mo>∈</mo><mo stretchy="false">(</mo><mn mathvariant="normal">0

1</mn><mo stretchy="false">)</mo><mo>

</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mrow><mi>v</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>=</mo><mi>μ</mi><mi>u</mi><mo>

</mo><mtext> </mtext><mi>t</mi><mo>∈</mo><mo stretchy="false">(</mo><mn mathvariant="normal">0

1</mn><mo stretchy="false">)</mo><mo>

</mo></mtd></mtr></mtable></mrow></mfenced></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156449&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156468&type=

38.94666672

8.32555580

admits at least one positive solution for any

</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo><mo>.</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156469&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121156463&type=

11.99444389

2.96333337

关键词

Keywords

references

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