Abstract
This article is concerned with the description of the entire solutions of several Fermat type partial differential-difference equations (PDDEs) μf(z)+λfz1(z)2+[αf(z+c)−βf(z)]2=1, and μf(z)+λ1fz1(z)+λ2fz2(z)2+[αf(z+c)−βf(z)]2=1, where fz1(z)=∂f∂z1 and fz2(z)=∂f∂z2, c=(c1,c2)∈C2, α,β,μ,λ,λ1,λ2,c1,c2 are constants in C. Our theorems in this paper give some descriptions of the forms of transcendental entire solutions for the above equations, which are some extensions and improvement of the previous theorems given by Xu, Cao, Liu, and Yang. In particular, we exhibit a series of examples to explain that the existence conditions and the forms of transcendental entire solutions with a finite order of such equations are precise.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference39 articles.
1. On the equation fn + gn = 1;Gross;Bull. Am. Math. Soc.,1966
2. Montel, P. Lecons sur les Familles Normales de Fonctions Analytiques et Leurs Applications, 1927.
3. On an integral function of an integral function;Pólya;J. Lond. Math. Soc.,1926
4. Ring-theoretic properties of certain Hecke algebra;Taylor;Ann. Math.,1995
5. Modular elliptic curves and Fermats last theorem;Wiles;Ann. Math.,1995
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