亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        Meromorphic Solutions of a Type of Complex Differential-Difference Equations

        2020-07-28 01:13:18RENGuozhen任國(guó)珍GAOLingyun高凌云
        應(yīng)用數(shù)學(xué) 2020年3期
        關(guān)鍵詞:凌云

        REN Guozhen(任國(guó)珍),GAO Lingyun(高凌云)

        (Department of Mathematics,Jinan University,Guangzhou 510632,China)

        Abstract: Using Nevanlinna theory of the value distribution of meromorphic functions,we investigate the properties and expression of meromorphic solutions of a type of complex differential-difference equation,and we obtain some results,which are the extensions of complex difference equations to differential-difference equations.Example shows that our results are meaningful.

        Key words: Complex differential-difference equation;Meromorphic solution;Value distribution

        1.Introduction

        Letf(z) be a meromorphic function in the whole complex plan C.We assume that the reader is familiar with the standard notation and results of the Nevanlinna theory of meromorphic functions[1?2],such as the characteristic functionT(r,f),proximity functionm(r,f),counting functionN(r,f).

        The notationS(r,f)denotes any quantity that satisfies the condition:S(r,f)=o(T(r,f))asr →∞possibly outside an exceptional setEofrof finite linear measure∞.A meromorphic functiona(z) is called a small function off(z) if and only ifT(r,a(z))=S(r,f).Moreover,we use the notation degf Pfor the degree ofP(z,f) with respect tofand the order offis defined by

        Many papers investigate solutions of some types of complex differential equations,and obtain some results[3?8].Recently,there has been renewed interests in meromorphic solutions of complex difference equations,in addition to the complex differential equation.Many authors have investigated complex difference equations,and obtained some results[9?15].

        In 2005,Laine and Rieppo[14]considered a type of complex differential equations of the following form

        wherePandQare relatively prime polynomials infover the field of rational functions,the coefficientsαJare rational functions andq=degf Q >0.They obtained the following results.

        Theorem A[14]Assumef(z) is a transcendental meromorphic solution of the above difference equation,andf(z) has finitely many poles,it must be of the form

        f(z)=r(z)eg(z)+s(z),

        wherer(z) ands(z) are rational functions andg(z) is a transcendental entire function satisfying a difference equation of the form either

        2.Some Lemmas

        In order to prove our results,we need the following lemmas.

        Lemma 2.1[14]Letfbe a non-constant meromorphic function and letP(z,f),Q(z,f)be two polynomials infwith meromorphic coefficients small relative tof.IfPandQhave no common factors of positive degree infover the field of small functions relative tof,then

        Remark 2.1[14]Iff(z) is a transcendental meromorphic function andP(z,f),Q(z,f)have rational coefficients,thenP(z,f(z))andQ(z,f(z))has only finitely many common zeros.

        Lemma 2.2[16]Letf(z) be a meromorphic function and letΦbe given by

        3.Main Results and Proofs

        In this paper,letting

        P(z,f)=ap(z)fp+ap?1(z)fp?1+···+a0(z),

        where

        猜你喜歡
        凌云
        保留一點(diǎn)兒焦慮感
        做人與處世(2022年2期)2022-05-26 22:34:53
        著名女詩(shī)人 池凌云
        鴨綠江(2020年23期)2020-10-13 13:29:06
        梅苑人物 瞿凌云
        Exploration on Integrative Traditional Chinese and Western Medicine Strategy for Treating Patients of Lung Cancer over 80 Years Old
        Q萌霸氣凌云秀
        群賢畢至少長(zhǎng)咸集
        陶山(2018年4期)2018-12-28 09:19:08
        Therapeutic observation of acupuncture plus tuina for cervical vertigo
        威龍凌云
        航空世界(2018年12期)2018-07-16 08:34:30
        洱海太湖石
        唯有凌云多壯“質(zhì)”
        軍工文化(2017年12期)2017-07-17 06:08:02
        国产亚洲av另类一区二区三区| 免费在线亚洲视频| 免费无码a片一区二三区| 精品国产av 无码一区二区三区 | 精品一区中文字幕在线观看| 怡红院av一区二区三区| 国产精品白浆一区二小说| 久久亚洲Av无码专区| 亚洲国产免费公开在线视频| 一区二区三区日本高清| 岛国熟女精品一区二区三区| 久久久久久曰本av免费免费| 成人国产精品999视频| 狠狠干视频网站| 蜜桃一区二区三区在线视频| 亚洲成人av大片在线观看| 国产一区二区视频免费在线观看| 色www视频永久免费| 国产一国产一级新婚之夜| 91中文人妻丝袜乱一区三区| 亚洲长腿丝袜中文字幕| 性无码一区二区三区在线观看| 久久久久久无码av成人影院| 国产精品黄在线观看免费软件| 中文字幕乱码亚洲无线精品一区| 日本肥老熟妇在线观看 | 免费观看黄网站在线播放| 最新国产女主播福利在线观看| 亚洲一区二区av偷偷| 视频国产一区二区在线| 国产精品午夜夜伦鲁鲁| 国产免费av片在线播放| 亚洲熟妇无码av另类vr影视| AV无码中文字幕不卡一二三区| 日本二区三区视频在线观看| 91国产精品自拍在线观看| 亚洲精品久久| 九九在线视频| 国产精品又污又爽又色的网站| 女人下边被添全过视频| 国产美女遭强高潮网站|