一类中立型偏微分方程的振动性

OSCILATION THEOREMS OF THE SOLUTION OF NEUTRAL PARTIAL DIFFERENTIAL EQUATION

本文研究了一类中立型偏微分方程(?)~2 /(?)t^2[u(x,t)+sum from i=1 to m(λ_i(t)u(x,t-τ_i)])+(?)/(?)t[u(x,t)+sum from i=1 to m(λ_i(t)u(x,t-τ_i)])+P(x,t)u(x,t)+sum from j=1 to m_1(P_j(x,t)u(x,t-δ_j))=△u(x,t)+sum from k=1 to m_2(a_k(t)△u(x,t-p_k)(1)解的振动性,其中(x,t)∈Ω×(0,+∞)≡G,Ω(?)R^n是有界域,(?)Ω逐片光滑,△u=sum from k=1 to n((?)~2/(?)x_k^2u(x,t)),我们获得了方程(1)在不同边界条件下的所有解振动的充分条件,并给出这些充分条件应用的实际例子.

In the paper we discussed the oscillation of the solutions of neutral partial differental equation of the form.Where (x,t)∈Ω×(0,∞)≡G, Ω Rn is a bounded domain with a piecewise smooth boundary. △u =u(x,t) ,and obtain the sufficient comditions of oscillation of all solution(1).