中立型抛物边值问题解的Hunt-Yorke型定理

Hunt Yorke′s Theorem of Solutions for Neutral Parabolic Boundary Value Problems

讨论了非线性中立型抛物偏泛函微分方程系统ｔ〔ｕｉ（ｘ，ｔ）－Ｐ（ｔ）ｕｉ（ｘ，ｔ－σ（ｔ））〕＋Ａｉ（ｘ，ｔ）ｕｉ（ｘ，ｔ）＋ｍｊ＝１Ｂｉｊ（ｘ，ｔ）ｆｉｊ（ｕｊ（ｘ，ｔ－τ））＝Ｃｉ（ｔ）Δｕｉ（ｘ，ｔ）＋ｍｊ＝１Ｄｉｊ（ｔ）Δｕｉ（ｘ，ｔ－ｒｊ），ｉ＝１，２，…，ｍ，（ｘ，ｔ）∈Ω×（０，∞）≡Ｇ，其中ΩＲｎ是具有逐片光滑边界的有界区域，Δｕｉ（ｘ，ｔ）＝ｎｈ＝１２ｘ２ｈｕｉ（ｘ，ｔ），ｉ＝１，２，…，ｍ．

The oscillation of solutions for systems of nonlinear neutral parabolic partial functional differential equation of the formtu i(x,t)-P(t)u i(x,t-σ(t))+A i( x,t )u i(x,t)+mj=1B ij (x,t)f ij (u j(x,t-τ))=C i(t) Δ u i(x,t)+mj=1D ij (t) Δ u i(x,t-r j),i=1,2,…,m,(x,t)∈Ω×(0,∞)≡Gis discussed,where Ω is a bounded domain in R n with piece wise smooth boundary,Δu i(x,t)=nh=1 2x 2 hu i(x,t),i=1,2,…,m.Sufficient conditions are obtained for oscillation of solutions of systems.