六盘水师范学院学报2026，Vol.38Issue(1)：78-84,7.DOI:10.16595/j.1671-055X.2026.01.007
Fermat型q-差分微分方程的整函数解
Entire Solutions of Fermat Type q-Difference Differential Equations
摘要
Abstract
Utilizing Nevanlinna and complex differential-difference equations theory,the precise ana-lytic forms of transcendental entire solutions are explored for Fermat type equations of the form[f(K)(z)]2+[f(qz+c)-f(z)]2=Q(z)involving q-difference and derivatives.Firstly,system of equations sat-isfying the solution are obtained by Hadamard factorization theorem,and the concrete forms of f(K)(z)and f(qz+c)-f(z)are calculated.Secondly,in the equation that the sum of the function fj(z)(j=1,2,3)is 1,the uniqueness theorem of meromorphic function is used to judge that the two functions in fj(z)(j=1,2,3)are identical to 1,and the discussion is divided into two cases.Finally,in each case,k is odd and even,and the relationship between the variables is obtained.Thereby leads to more ideas and techniques for studying solutions of complex differential-difference equations in future research.关键词
Fermat型q-差分微分方程/整函数解/有限级Key words
Fermat-type q-difference differential equations/Entire solutions/Finite order分类
数理科学引用本文复制引用
杨龙燕,杨祺,刘晓文..Fermat型q-差分微分方程的整函数解[J].六盘水师范学院学报,2026,38(1):78-84,7.基金项目
新疆维吾尔自治区自然科学基金项目"关于费马型复微分-差分方程整函数解的研究"(2024D01A91) （2024D01A91）
国家自然科学基金项目"正规族理论及其应用"(11961068). （11961068）
