We study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions o...We study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant.For a static vacuum(Mn,g,V),we also compute the asymptotic expansions of g and V at conformal infinity.展开更多
The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN：{atu-xu ＋ b ·▽xu ＋ au ＋ V（t,x）v = Hv（t,x,u,v）,-atv-xv-b·▽xv ＋ av ＋ V（...The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN：{atu-xu ＋ b ·▽xu ＋ au ＋ V（t,x）v = Hv（t,x,u,v）,-atv-xv-b·▽xv ＋ av ＋ V（t,x）u = Hu（t,x,u,v）,where z =（u,v）：R × RN → Rm × Rm,a 〉 0,b =（b1,···,bN） is a constant vector and V ∈ C（R × RN,R）,H ∈ C1（R × RN × R2m,R）.Under suitable conditions on V（t,x） and the nonlinearity for H（t,x,z）,at least one non-stationary homoclinic solution with least energy is obtained.展开更多
For the infinite delay difference equations of the general form, two new uniform asymptotic stability criteria are established in terms of the discrete Liapunov functionals.
基金supported by National Natural Science Foundation of China (Grant Nos.10725101 and 10990013)
文摘We study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant.For a static vacuum(Mn,g,V),we also compute the asymptotic expansions of g and V at conformal infinity.
基金Project supported by the National Natural Science Foundation of China (No.10971194)the Zhejiang Provincial Natural Science Foundation of China (Nos.Y7080008,R6090109)the Zhejiang Innovation Project (No.T200905)
文摘The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN：{atu-xu ＋ b ·▽xu ＋ au ＋ V（t,x）v = Hv（t,x,u,v）,-atv-xv-b·▽xv ＋ av ＋ V（t,x）u = Hu（t,x,u,v）,where z =（u,v）：R × RN → Rm × Rm,a 〉 0,b =（b1,···,bN） is a constant vector and V ∈ C（R × RN,R）,H ∈ C1（R × RN × R2m,R）.Under suitable conditions on V（t,x） and the nonlinearity for H（t,x,z）,at least one non-stationary homoclinic solution with least energy is obtained.
基金Project supported by the National Natural Science Foundation of China (No. 19831030).
文摘For the infinite delay difference equations of the general form, two new uniform asymptotic stability criteria are established in terms of the discrete Liapunov functionals.
