Factorization of entire solutions of some algebraic differential equations

[摘要] We investigate the factorization of entire solutions of the following algebraic differential equations: b(n)(z)f(in)(f')(jn) + b(n-1)(z)f(in-1)(f')(jn-1) + (...) + b(0)(z)f(i0) (f')(j0) = b(z), where n is an element of N is a natural number, i(s) >= 0, j(s) >= 0, i(s) + j(s) > 0 (0 <= s <= n) are the integers, and b(i) (z) not equal 0 (0 <= i <= n) are the polynomials. Moreover, the results enable us to provide new criteria/proofs of primeness or pseudo-primeness for certain well-known classes of entire functions. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01

[关键词] entire solutions;pseudo-prime;algebraic differential equation;polynomial factor