摘要
本文研究带有阻尼项的双曲型时滞偏微分方程 2 t2 u(x,t) +m(t) u t=a(t)△ u(x,t) +b(t)△ u(x,ρ(t) ) -q(t) f (u(x,σ(t) ) ,(x,t)∈ G≡Ω× R+ (1 )其中 ,R+=[0 ,+∞ ) ,Ω是一个具有逐段光滑边界的有界区域 .利用平均法和微分不等式方法得到方程 (1 )的若干新的振动准则 .
In this paper we study partial diffevential equations with deviating arguments and damped terms of neutral type of the form 2t\+2u(x,t)+m(t)ut=a(t)△u(x,t)+b(t)△u(x,ρ(t))-q(t)f(u(x,σ(t)), (x,t)∈G≡Ω×R\-+(1)where Ω is a bounded domain with piecewise smooth boundary, and R\-+=\[0,+∞).[WTBZ] With average method and differential inequality method used, some new criteria for oscillation of equation (1) are obtained.
出处
《数学的实践与认识》
CSCD
2000年第3期331-338,共8页
Mathematics in Practice and Theory
关键词
微分不等式
振动性
阻尼项
偏泛函微分方程
解
hyperbolic type
partial differential equation
differential inequality
deviating arguments
oscillation
