中立型双曲微分方程解的振动性

Oscillation of Solutions of Neutral Hyperbolic Differential Equations

研究中立型时滞微分方程 2 t2 [u(x ,t) +p(t)u(x ,t-τ) ]=a(t)Δu(x ,t) - q(t) f(u(x ,σ(t) ) ) (1)(x ,t) ∈Ω×R+ ≡G 其中 ,R+ =[o ,+∞ ) ;Ω是具有逐段光滑边界的有界区域 ,建立了方程 (1)的一切解均振动的新的充分条件 ,推广了文

We stuyd the time-lag partial differential equations with neutral type of the form 2t 2[u(x,t)+p(t)u(x,t-τ)]=a(t)Δu(x,t)-q(t)f(u(x,σ(t)))(1) (x,t)∈Ω×R +≡G where Ω is a bounded domain with a piecewise smooth boundary,and R +=[0,+∞).New sufficient conditions for oscillations of all solutions of equation(1) are obtained,which generalized the conclusions of paper [1].