一类中立型时滞抛物偏微分方程的强迫振动性

研究了一类中立型时滞抛物偏微分方程:t(u(x,t)-pu(x,t-τ))-∑rk=1ak(t)Δu(x,t-ρk(t))+∑mj=1qj(t)u(x,t-σj(t))=e(x,t),的强迫振动性(其中(x,t)∈Ω×0,∞)≡G,Ω是n维欧几里得空间Rn中带有逐段光滑边界Ω的有界区域,Δ是Rn中带有三类不同边值条件的拉普拉斯算子,强迫项e(x,t)是定义在G上的一个振荡函数),给出了一些新的振动性判据,这些结果推广了已知的一些结论.

Forced Oscillation for a Class of Neutral Delay Parabolic Partial Functional Differential Equations

We investigate the forced oscillation for a class of neutral delay parabolic partial differential equations of the form:t(u(x,t)-pu(x,t-τ))∑rk=1a_k(t)Δu(x,t-ρ_k(t))+∑mj=1q_j(t)u(x,t-σ_j(t))=e(x,t),where(x,t)∈Ω×0,∞)≡G,Ω is a bounded domain in R~nwith a piecewise smooth boundary Ω,and Δ is the Laplacian in Euclidean n-space R~n with three differential boundary conditions, and the forcing term e(x,t) is a oscillatory function defined on G.Some new oscillatory criteria are obtained.Our results extended some known conclusions.