| Consider the impulsive difference equationwhere ak>0,bk>0,ck>0,p(n)≥0,p(n)(?)0,0012<…k<…and (?) nk=∞,(?)∈N,△x(n)=x(n+1)-x(n)．Our main results as following:THEOREM 1．Assume that(H1):(n1-n0)+b1(n2-n1)+b1b2(n3-n2)+…+b1b2b3…bm(nm+1-nm)+…=∞,(H2):(n1-n0)+c1(n2-n1)+c1c2(n3-n2)+…+c1c2c3…cm(nm+1-nm)+…=∞,hold,and sum from k=1 to∞|ak-1|converges,(?)n(2)p(n)=∞．Then every bounded solution of above equation either oscillates or tends asymptotically tozero with fixed sign．THEOREM 2．Assume that (H1) and (H2) hold,and sum from n=1 to∞|an-1| converges,(?)p(n)=∞,ck/(ak-1)≤1,nk-nk-1≥(?)+1．Then every solution of above equation either oscillates or tends asymptotically to zero withfixed sign．THEOREM 3．Assume that(H1) and (H2) hold,(?)sum from s=n-(?) to n-1 (s-n)(2)p(s)>2,or(?)sum from s=n-(?) to n-1 (s-n+(?))(2)p(s)>2, (?)Then every bounded solution of above equation oscillates．...
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