具正负系数非线性中立型差分方程的稳定性

Stability of nonlinear neutral difference equations with positive and negative coefficients

讨论一类具正负系数的非线性中立型差分方程△(xn-cnxn-k)+pnf(xn-)-qng(xn-r)=0,n∈N(0),其中k,l,r∈N(1),f,g∈C(R,R),且f(0)=g(0)=0;{cn}为实数序列,{pn},{qn}为非负实数序列。利用反证法和分析的方法,结合均值不等式,给出了该方程零解一致稳定的充分条件。推广和改进了具正负系数的线性中立型差分方程已有的相关结果。

Abstract： A class of nonlinear neutral difference equation with positive and negative coefficients △（xn-cnxn-k）＋pnf（xn-）-qng（xn-r）=0,n∈N（0）, discussed in this paper, where k,l,r∈N（1）,f,g∈C（R,R）, and f（0）= g（0） = 0; （cn} is asequence of real numbers and {pn},{qn}are sequences of nonnegative real numbers. By absurdity and analysis methods, combined with the mean value inequality,sufficient conditions for the uniform stability of the zero solution of this equation are given. The existing results in the linear neutral difference equation with positive and negative coefficients are extended and improved.