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Oscillation of Solutions of Neutral Partial Functional Differential Equations

机译:中立型偏泛函微分方程解的振动性。

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摘要

Sufficient conditions are established for the oscillation of solutions of neutral partial functional differential equations of the form (partial deriv)/(partial deriv t) [p(t)(partial deriv)/(partial deriv t) (u(x,t) + sum from i=1 to l of #lambda#_i(t)u(x,t - #tau#_i))] = a(t) triangle open u (x,t) + sum from k=1 to s of a_k (t) triangle open u (x,t - #rho#_k(t)) - q(x,t)u(x,t) - sum from j=1 to m of q_j(x,t)f_j(u(x,t - #pho#_j)), (x,t) implied by #OMEGA# * [0, infinity) ident to G, where #OMEGA# is a bounded domain in R~N with a piecewise smooth boundary partial deriv #OMEGA# and triangle open is the Laplacian in the Euclidean N-space R~N.
机译:为(偏导数/(偏导数t)[[p(t)(偏导数)/(偏导数t)(u(x,t)) +从i = 1至#的总和#lambda#_i(t)u(x,t-#tau#_i))] = a(t)三角形开u(x,t)+从k = 1至s的总和a_k(t)三角形的u开口u(x,t-#rho#_k(t))-q(x,t)u(x,t)-q_j(x,t)f_j从j = 1到m的和(u(x,t-#pho#_j)),#OMEGA#* [0,infinity)隐含的(x,t)等同于G,其中#OMEGA#是R〜N中的有界区域,具有分段平滑边界偏导数#OMEGA#和三角形开路是欧几里得N空间R〜N中的拉普拉斯算子。

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