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
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.
