具有连续变量的脉冲偏差分方程解的振动性

OSCILLATION OF SOLUTIONS OF IMPULSIVE PARTIAL DIFFERENCE EQUATION WITH CONTINUOUS VARIABLE

考虑一类具有连续变量的脉冲偏差分方程A(x+τ,y)+A(x,y+τ)-A(x,y)+p(x,y)A(x-rτ,y-lτ)=0,x≥x0;y≥y0-τ,x≠xk,A(xk+τ,y)+A(xk,y+τ)-A(xk,y)=bkA(xk,y),y∈[y0-τ,∞),k∈N(1).其中p(x,y)≥0是[x0,∞)×[y0-τ,∞)上的非负连续函数,τ>0,bk是常数,r和l是正整数,0≤x0<x1<…<xk<…,且kl→im∞xk=∞.获得了此类方程所有解是振动的充分条件.

We obtain sufficient conditions for oscillation of all solutions of the impulsive partial difference equation with continuous variable A（x＋τ,y）＋A（x,y＋τ）-A（x,y）＋p（x,y）A（x-rτ,y-lτ）=0,x≥x0;y≥y0-τ,x≠xk,A（xk＋τ,y）＋A（xk,y＋τ）-A（xk,y）=bkA（xk,y）,arbitary y∈[y0-τ,∞）,k∈N（1）.Where p（x,y）≥0 is continuous on [x0,∞）×[y0-τ,∞）,τ0,bk are constants,r and l are positive integers,0≤x0x1…xk… with k→∞limxk=∞.