差分-微分方程的Liouville解
Liouvillian Solutions of Difference-Differential Equations
摘要：
对于一个域k $with an automorphism σand a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y) = AY, δ(Y) = BY} over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x,t), σ(x) = x+1, δ= d/dt$和系统的大小是一个素数。
英文摘要：
For a field k$with an automorphism σand a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y) = AY, δ(Y) = BY} over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x,t), σ(x) = x+1, δ= d/dt$ and the size of the system is a prime.
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