Fermat型q-差分微分方程的整函数解

摘要

采用值分布理论及复微分-差分方程理论,探讨了带有微分项及q-差分项(f(K)(z))2 +[f(qz + c)−f(z)]2 = Q(z) 的Fermat型方程超越整函数解的解析形式。根据Hadamard因子分解定理得到满足解的一个方程组,计算出f(K)(z)与f(qz + c)−f(z)的明确表达形式。在函数fj(z)(j = 1,2,3)求和为1的方程中,基于亚纯函数的唯一性定理推断fj(z)(j = 1,2,3)中的两个函数恒等于1,并分两种情形进行了探讨,系统考察了k在所有可能取值情况下的奇偶性分布特征,得到了各个变量之间的关系,为以后复微分-差分方程解的研究提供了更多思路和技巧。

关键词

Fermat型q-差分微分方程 / 整函数解 / 有限级

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基金资助

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)

国家自然科学基金项目“正规族理论及其应用”(11961068)