在Rn(n≥1)的单位球Bn上研究带有第一类边值条件的果蝇模型:Δu+λf(u)=0for x∈Bnu=0 for x∈Bn(其中λ>0,f=u(-1+be-au))的精确解的个数,并得到了精确的全局分支结构.利用Rabinowitz从单特征值出发的分支定理,得到该方程的解的结...在Rn(n≥1)的单位球Bn上研究带有第一类边值条件的果蝇模型:Δu+λf(u)=0for x∈Bnu=0 for x∈Bn(其中λ>0,f=u(-1+be-au))的精确解的个数,并得到了精确的全局分支结构.利用Rabinowitz从单特征值出发的分支定理,得到该方程的解的结构,特别地,得到了方程的正解的存在性及正解的个数等结果.这些结果将在生物经济中有广泛的应用.展开更多
Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ...Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ?t ?x t = 0 : u = f(x). We let M = sup |f (x)| < +∞. x∈R The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t,x) for all t ∈ R, provided that +∞ |f (x)|dx ≤ ε, ?∞ +∞ ε |f(x)|dx ≤ . M∞展开更多
The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the give...The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).展开更多
文摘在Rn(n≥1)的单位球Bn上研究带有第一类边值条件的果蝇模型:Δu+λf(u)=0for x∈Bnu=0 for x∈Bn(其中λ>0,f=u(-1+be-au))的精确解的个数,并得到了精确的全局分支结构.利用Rabinowitz从单特征值出发的分支定理,得到该方程的解的结构,特别地,得到了方程的正解的存在性及正解的个数等结果.这些结果将在生物经济中有广泛的应用.
基金Project supported by the National Natural Science Foundation of China (No.10225102) the 973 Project of the Ministry of Science and Technology of China and the Doctoral Programme Foundation of the Ministry of Education of China.
文摘Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ?t ?x t = 0 : u = f(x). We let M = sup |f (x)| < +∞. x∈R The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t,x) for all t ∈ R, provided that +∞ |f (x)|dx ≤ ε, ?∞ +∞ ε |f(x)|dx ≤ . M∞
文摘The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).
