脉冲偏差分方程的振动性

Oscillation of Impulsive Partial Difference Equation

关键词:  偏差分方程  振动解  脉冲

Key words:  partial difference equation  oscillatory solution  impulsive

摘要:

获得脉冲偏差分方程A_m+1,n+A_m,n+1-A_m,n+p_mnA_m-r,n-l=0,m ≥ m₀,n ≥ n₀-1,m≠m_k,A_mk+1,n+A_mk,n+1-A_mk,n=b_kA_mk,n,∀n ≥ n₀-1,k∈N(1),所有解振动的充分条件,其中{p^mn}是一个双指标序列,对m ≥ m₀,n ≥ n₀-1,有p^mn ≥ 0且不恒为零,{b_k}是实数序列,r,l是正整数,0 ≤ m₀ ≤ m₁ < … < m_k < …满足lim_k→∞m_k=∞.

Abstract:

By employing arithemetic mean-geometric mean inequality and partial difference inequality, we obtain sufficient conditions for oscillation of all solution of the impulsive partial difference equation A_{m+1, n}+A_{m, n}+1-A_{m, n}+p_mnA_{m-r, n-l}=0, m ≥ m₀, n ≥ n₀-1, m≠m_k, A_{mk+1, n}+A_{mk, n+1}-A_{mk, n}=b_kA_{mk, n}, ∀n ≥ n₀-1, k∈N (1), where {p^mn} is a double sequence and p^mn ≥ 0 and not identically zero, for m ≥ m₀, n ≥ n₀-1, {b_k} is a real sequence, r, l are positive integers, 0 ≤ m₀ ≤ m₁ < … < m_k < … with lim_k→∞m_k=∞.