一类时滞双曲型微分方程解的振动性

OSCILLATION FOR SOLUTIONS OF CERTAIN DELAY HYPERBOLIC DIFFERENTIAL EQUATIONS

利用广义Riccati变换 ,建立了下列时滞双曲型微分方程 2 t2 u(x ,t) =a(t)Δu(x ,t) + sk =1ak(t)Δu(x ,t- ρk) - mj =1qj(x,t)u(x,t-σj)解的振动的若干充分条件 ,其中 (x ,t)∈Ω× [0 ,∞ )≡G ,Ω是RN中具有逐片光滑边界 Ω的有界区域 ,Δu(x ,t) = Nr=1 2 u(x ,t) x2r.

By using a generalized Riccati transformation, some sufficient conditions are established for the oscillation of solutions of delay hyperbolic differential equations of the form ~2 t^2u(x,t) =a(t)Δu(x,t)+sk=1a_k(t)Δ u(x,t-ρ_k)-mj=1q_j(x,t)u(x,t-σ_j), where (x,t)∈Ω×[0,∞)≡G, Ω is a bounded domain in R^N with a piecewise smooth boundary Ω and Δ is the Laplacian in Euclidean N-space R^N.