Necessary and sufficient conditions for oscillation of first-order nonlinear neutral difference equations

作者：Tang, X H^*; Lin, Xiaoyan

来源：Computers & Mathematics with Applications, 2008, 55(6): 1279-1292.

DOI：10.1016/j.camwa.2007.06.009

• first-order neutral difference equations
• superlinear
• sublinear
• oscillation
• necessary and sufficient conditions

In this paper, we prove that every solution of the first-order nonlinear neutral difference equation Delta(x(n)-px(n-tau))+q(n) (m)Pi(j=1)vertical bar x(n-sigma j)vertical bar(beta j) sign(x(n-sigma 1))=0, n >= n(0)
oscillates if and only if
(infinity)Sigma(s=n0) q(s) exp [tau(-1) ln p((m)Sigma(j=1) beta(j)-1)s]=infinity when ((m)Sigma(j=1)beta(j)-1)ln p<0, and
(infinity)Sigma(s=n0) q(s) =infinity,
when ((m)Sigma(j=1)beta(j)-1)ln p>0, where p, beta(j)>0, tau > 0 and sigma(j) >= 0 are integers, j=1,2,...,m,q(n)>= 0,n >= 0.

• 出版日期2008-3
• 单位中南大学