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On Entire Solutions of Partial Differential-Difference Equations in ![]()
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Mathematics | 更新时间：2026-10-29
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On Entire Solutions of Partial Differential-Difference Equations in
- Wuhan University Journal of Natural Sciences Vol. 31, Issue 5, Pages: 429-436(2026)
- 作者机构：
苏州科技大学 数学科学学院， 江苏 苏州 215009
- 作者简介：
WANG Anqi, female, Master candidate, research direction: complex analysis. E-mail: 18862003465@163.com
E-mail: alexehuang@sina.com
- 基金信息：
DOI：10.1051/wujns/2026315429
CLC： O174.5Received：11 March 2025，
Published：24 October 2026
- 稿件说明：
移动端阅览
王安琪,黄志刚.C2上偏微分-差分方程整函数解的研究[J].武汉大学学报自然科学英文版,2026,31(05):429-436.
WANG Anqi, HUANG Zhigang. On Entire Solutions of Partial Differential-Difference Equations in C2[J]. Wuhan Univ J of Nat Sci, 2026, 31(5): 429-436.
王安琪,黄志刚.C2上偏微分-差分方程整函数解的研究[J].武汉大学学报自然科学英文版,2026,31(05):429-436. DOI： 10.1051/wujns/2026315429.
WANG Anqi, HUANG Zhigang. On Entire Solutions of Partial Differential-Difference Equations in C2[J]. Wuhan Univ J of Nat Sci, 2026, 31(5): 429-436. DOI： 10.1051/wujns/2026315429.
On Entire Solutions of Partial Differential-Difference Equations in ![]()
![]()
摘要
本文主要研究了
<math id="M7"><msup><mrow><mi mathvariant="double-struck">C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275845&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275807&type=
3.80999994
2.96333337
上带有多项式系数的费马型偏微分-差分方程
<math id="M8"><msup><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msup><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><mi>z</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfrac><mrow><mo>∂</mo><mi>f</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msup><mrow><mfrac><mrow><msup><mrow><mo>∂</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>f</mi></mrow><mrow><mo>∂</mo><msup><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>=</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></msup></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275870&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275846&type=
69.99111176
8.46666718
的有限级超越整函数解的存在性和精确表达式，其中
<math id="M9"><mi>P</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275872&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275871&type=
6.34999990
3.38666677
，
<math id="M10"><mi>Q</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275886&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275885&type=
6.63222170
3.38666677
，
<math id="M11"><mi>g</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275876&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275887&type=
5.92666674
3.38666677
为非零多项式。
Abstract
In this paper
we mainly study the existence and precise form of finite order transcendental entire solutions to the Fermat-type partial differential-difference equation with polynomial coefficients
<math id="M3"><msup><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msup><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><mi>z</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfrac><mrow><mo>∂</mo><mi>f</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow><mrow><mo>∂</mo><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msup><mrow><mfrac><mrow><msup><mrow><mo>∂</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>f</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow><mrow><mo>∂</mo><msup><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>=</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></msup></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275814&type=
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65.89889526
7.47888899
where
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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275815&type=
5.36222219
2.96333337
<math id="M5"><mi>Q</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275803&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275817&type=
5.64444447
2.96333337
<math id="M6"><mi>g</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275832&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121275804&type=
5.07999992
2.96333337
are non-zero polynomials.
关键词
Keywords
references
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