删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

Fermat型偏微差分方程组的整函数解

本站小编 Free考研考试/2021-12-27

Fermat型偏微差分方程组的整函数解 徐洪焱1, 杨连忠21. 上饶师范学院数学与计算机学院 上饶 334001;
2. 山东大学数学学院 济南 250100 Entire Solutions of Several Fermat Type Systems of Partial Differential Difference Equations Hong Yan XU1, Lian Zhong YANG21. School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001, P. R. China;
2. Department of Mathematics, Shandong University, Ji'nan 250100, P. R. China
摘要
图/表
参考文献
相关文章

全文: PDF(530 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)
摘要利用多变量Nevanlinna值分布理论与Nevanlinna理论的差分模拟结果,讨论了几类多变量复域Fermat型偏微差分方程组解的性质,得到了方程组有限超越整函数解的存在性条件与具体形式,推广改进了高凌云、曹廷彬、刘凯等人的结果,给出例子说明多变量与单变量方程组有限级超越整函数解之间的差异.
服务
加入引用管理器
E-mail Alert
RSS
收稿日期: 2020-04-28
MR (2010):O174
基金资助:国家自然科学基金资助项目(11561033,11371225);江西省自然科学基金(20181BAB201001)及江西省教育厅科技项目(GJJ190876,GJJ191042,GJJ190895)
作者简介: 徐洪焱,E-mail:xuhongyanxidian@126.com;杨连忠,E-mail:lzyang@sdu.edu.cn
引用本文:
徐洪焱, 杨连忠. Fermat型偏微差分方程组的整函数解[J]. 数学学报, 2021, 64(6): 909-932. Hong Yan XU, Lian Zhong YANG. Entire Solutions of Several Fermat Type Systems of Partial Differential Difference Equations. Acta Mathematica Sinica, Chinese Series, 2021, 64(6): 909-932.
链接本文:
http://www.actamath.com/Jwk_sxxb_cn/CN/ http://www.actamath.com/Jwk_sxxb_cn/CN/Y2021/V64/I6/909


[1] Biancofiore A., Stoll W., Another proof of the lemma of the logarithmic derivative in several complex variables, In:Fornaess, J. (ed.) Recent developments in several complex variables, Princeton University Press, Princeton, 1981:29-45.
[2] Cao T. B., Xu L., Solutions of complex Fermat-type partial difference and differential-difference equations, Mediterr. J. Math., 2018, 15:1-14.
[3] Cao T. B., Xu L., Logarithmic difference lemma in several complex variables and partial difference equations, Ann. Mat. Pura Appl., 2020, 199(2):767-794.
[4] Cao T. B., Korhonen R. J., A new version of the second main theorem for meromorphic mappings intersecting hyper planes in several complex variables, J. Math. Anal. Appl., 2016, 444:1114-1132.
[5] Chiang Y. M., Feng S. J., On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane, Ramanujan J., 2008, 16(1):105-129.
[6] Gao L. Y., Entire solutions of two types of systems of complex differential-difference equations, Acta Math. Sinica, Chinese Series, 2016, 59:677-685.
[7] Gross F., On the equation fn+gn=1, Bull. Amer. Math. Soc., 1996, 72:86-88.
[8] Halburd R. G., Korhonen R. J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 2006, 314:477-487.
[9] Halburd R. G., Korhonen R. J., Finite-order meromorphic solutions and the discrete Painlevé equations, Proc. London Math. Soc., 2007, 9:443-474.
[10] Halburd R. G., Korhonen R. J., Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 2006, 31(2):463-478.
[11] Hu P. C., Malmquist type theorem and factorization of meromorphic solutions of partial differential equations, Complex Var., 1995, 27:269-285.
[12] Hu P. C., Yang C. C., Uniqueness of meromorphic functions on Cm, Complex Variables, 1996, 30:235-270.
[13] Hu P. C., Li P., Yang C. C., Unicity of Meromorphic Mappings, Advances in Complex Analysis and its Applications, Vol. 1. Kluwer Academic Publishers, Dordrecht, Boston, London, 2003.
[14] Korhonen R. J., A difference Picard theorem for meromorphic functions of several variables, Comput. Methods Funct. Theory, 2012, 12(1):343-361.
[15] Liu K., Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl., 2009, 359:384-393.
[16] Liu K., Cao T. B., Cao H. Z., Entire solutions of Fermat type differential-difference equations, Arch. Math., 2012, 99:147-155.
[17] Liu K., Yang L. Z., On entire solutions of some differential-difference equations, Comput. Methods Funct. Theory, 2013, 13:433-447.
[18] Liu K., Cao T. B., Entire solutions of Fermat type difference differential equations, Electron. J. Diff. Equ., 2013, 59:1-10.
[19] Liu M. L., Gao L. Y., Transcendental solutions of systems of complex differential-difference equations, Sci. Sinica Mathematica, 2019, 49:1-22.
[20] Montel P., Lecons sur les Familles Normales de Fonctions Analytiques et Leurs Applications, Gauthier-Villars, Paris, 1927, 135-136.
[21] Pólya G., On an integral function of an integral function, J. Lond. Math. Soc., 1926, 1:12-15.
[22] Rieppo J., On a class of complex functional equations, Ann. Acad. Sci. Fenn. Math., 2007, 32(1):151-170.
[23] Ronkin L. I., Introduction to the Theory of Entire Functions of Several Variables, Moscow:Nauka 1971(Russian); American Mathematical Society, Providence, 1974.
[24] Stoll W., Holomorphic Functions of Finite Order in Several Complex Variables, American Mathematical Society, Providence, 1974.
[25] Taylor R., Wiles A., Ring-theoretic properties of certain Hecke algebra, Ann. Math., 1995, 141:553-572.
[26] Wiles A., Modular elliptic curves and Fermats last theorem, Ann. Math., 1995, 141:443-551.
[27] Xu L., Cao T. B., Correction to:solutions of complex Fermat-type partial difference and differential-difference equations, Mediterr. J. Math., 2020, 17, Art. 8, pages, 1-4.
[28] Yang C. C., A generalization of a theorem of P. Montel on entire functions, Proc. Amer. Math. Soc., 1970, 26:332-334.
[29] Yang C. C., Li P., On the transcendental solutions of a certain type of nonlinear differential equations, Arch Math. Basel, 2004, 82:442-448.

[1]郑晓俊, 郇中丹, 刘君. 图像配准中方向场正则化模型的适定性和收敛性[J]. 数学学报, 2021, 64(3): 385-404.
[2]吴丽镐, 张然然, 黄志波. 一类微分差分方程的整函数解[J]. 数学学报, 2021, 64(3): 471-478.
[3]杜金金, 王昊. 推广的GDGH2系统的自相似解及爆破现象[J]. 数学学报, 2019, 62(1): 137-150.
[4]曾翠萍, 邓炳茂, 方明亮. 复微分-差分方程组的整函数解[J]. 数学学报, 2019, 62(1): 123-136.
[5]凌博, 刘永平. 用指数型整函数的最佳限制逼近[J]. 数学学报, 2017, 60(3): 389-400.
[6]高凌云. 两类复微分-差分方程组的整函数解[J]. 数学学报, 2016, 59(5): 677-684.
[7]刘慧芳, 毛志强. 整函数与其差分算子的唯一性定理[J]. Acta Mathematica Sinica, English Series, 2015, 58(5): 825-832.
[8]胡盛清, 王硕. 五体问题的中心构型及其相对平衡解[J]. Acta Mathematica Sinica, English Series, 2014, 57(6): 1199-1202.
[9]彭艳芳, 李必文. 一类奇异椭圆型方程变号解的存在性及非存在性[J]. Acta Mathematica Sinica, English Series, 2014, 57(2): 281-294.
[10]周文书, 魏晓丹, 秦绪龙. 一类奇异半线性椭圆方程解的不存在性[J]. Acta Mathematica Sinica, English Series, 2014, 57(1): 125-130.
[11]马如云, 陈瑞鹏, 李杰梅. 非线性Neumann问题正解的存在性[J]. Acta Mathematica Sinica, English Series, 2013, 56(3): 289-300.
[12]陈国旺. 一类N维非线性波动方程的Cauchy问题[J]. Acta Mathematica Sinica, English Series, 2012, 55(5): 797-810.
[13]姚庆六. 奇异非线性边值问题的经典Agarwal-O'Regan方法[J]. Acta Mathematica Sinica, English Series, 2012, 55(5): 903-918.
[14]王婷婷. Fibonacci 数列倒数的无穷和[J]. Acta Mathematica Sinica, English Series, 2012, 55(3): 517-524.
[15]王晋勋, 李兴民. O-解析函数紧致奇点的可去性[J]. Acta Mathematica Sinica, English Series, 2012, (2): 231-234.



PDF全文下载地址:

http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23872
相关话题/数学 系统 计算机 山东大学 数学学院

闂佺懓鐡ㄩ崝鎺旀嫻閻旂儤瀚氶柛娆嶅劚閺佲晠鎮跺☉杈╁帨缂佽鲸绻堝畷姘跺幢閺囥垻鍙愰柣鐘叉搐婢т粙鍩㈤懖鈺傚皫闁告洦鍓氶悘鎰版⒑閸撗冧壕閻㈩垰顕禍鍛婃綇椤愩垹骞嬮梺鍏煎劤閸㈣尪銇愰敓锟�40%闂佸湱绮崝鏍垂濮樿鲸灏庢慨妯垮煐鐏忣亪鏌ㄥ☉铏
闂佽浜介崝宀€绮诲鍥ㄥ皫婵ǹ鍩栫亸顏堟煛婢跺﹤鏆熸繛澶樺弮婵℃挳宕掑┑鎰婵炲濯寸紞鈧柕鍡楀暣瀹曪綁顢涢悙鈺佷壕婵ê纾粻鏍瑰⿰鍕濞寸姴鐗忕槐鏃堝箣閻樺灚鎯i梻渚囧亝閺屻劎娆㈤悙瀵糕枖闁绘垶蓱閹疯京绱掗弮鈧悷锔炬暜瑜版帞宓侀柛顭戝櫘閸氬懎霉閼测晛袥闁逞屽墯闁芥墳P婵炴潙鍚嬮懝楣冨箟閹惰棄鐏虫繝鍨尵缁€澶愭煟閳ь剙濡介柛鈺傜洴閺屽懎顫濆畷鍥╃暫闁荤姴娲よぐ鐐哄船椤掑倹鍋橀柕濞у嫮鏆犻梺鍛婂笒濡棃妫呴埡鍛叄闁绘劦鍓欐径宥夋煙鐎涙ḿ澧柟鐧哥秮楠炲酣濡烽妸銉︾亷婵炴垶姊瑰姗€骞冨Δ鍛櫖鐎光偓閸愭儳娈炬繛瀵稿缂嶁偓闁靛棗鍟撮幊銏犵暋閺夎法鎮�40%闂佸湱绮崝鏍垂濮樿泛违闁稿本绻嶉崵锕€霉閻欏懐绉柕鍡楀暟閹峰綊顢樺┑鍥ь伆闂佸搫鐗滈崜娑㈡偟椤栨稓顩烽悹浣哥-缁夊灝霉濠х姴鍟幆鍌炴煥濞戞ǹ瀚版繛鐓庡缁傚秹顢曢姀鐘电К9闂佺鍩栬彠闁逞屽墮閸婃悂鎯冮姀銈呯闁糕剝娲熼悡鈺呮⒑閸撗冧壕閻㈩垱鎸虫俊瀛樻媴鐟欏嫬闂梺纭呯堪閸庡崬霉濮椻偓閹囧炊閳哄啯鎯i梺鎸庣☉閼活垵銇愰崒鐐茬闁哄顑欓崝鍛存煛瀹撴哎鍊ら崯鍫ユ煕瑜庣粙蹇涘焵椤戣儻鍏屾繛鍛妽閹棃鏁冩担绋跨仭闂佸憡鐨滄担鎻掍壕濞达綁鏅茬花鎶芥煕濡や礁鎼搁柍褜鍏涚粈浣圭閺囩喓鈹嶉幒鎶藉焵椤戝灝鍊昋缂備礁鏈钘壩涢崸妤€违濞达綀娅i崣鈧繛鎴炴煥缁ㄦ椽鍩€椤戞寧绁伴柣顏呮尦閹椽鏁愰崶鈺傛儯闂佸憡鑹剧€氼剟濡甸崶顒傚祦闁告劖褰冮柊閬嶆煏閸☆厽瀚�