二阶拟线性时滞差分方程解的振动性与渐近性

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SECOND ORDER QUASILINEAR DELAY DIFFERENCE EQUATION

研究了二阶拟线性时滞差分方程Δ(rn(Δxn) σ) +f(n ,x(h1 (n) ) ,x(h2 (n) ) ,… ,x(hm(n) ) ) =0 ,n∈N(n0 ) ,(E)其中m≥ 1 ,N(n0 ) ={n0 ,n0 +1 ,n0 +2 ,… }的解的振动性与渐近性 .给出了方程 (E)的所有解振动与非振动的一些充要条件 .

The authors are dealing with the oscillatory and asymptotic behavior of solutions of second order quasilinear delay difference equation of the form  Δ (r-n( Δ x-n)~σ)+f(n,x(h-1(n)),x(h-2(n)),... ,x(h-m(n)))=0, n∈N(n-0),( E) where m≥1,N(n-0)={n-0,n-0+1,...}. Some necessary and sufficient conditions for equation (E) to be oscillatory and nonoscillatory are given.