In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke compari...In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).展开更多
In this artical the existence, stability and asymptoticity of periodic solutionfor Abel equation :as well as ones for its special cases are discussed, where a(t), b(t), c(t) and d(t)are real periodic functions.
In this paper,we deal with the existence of unbounded orbits of the mapping where n is a positive integer,c is a constant andμ（θ）is a 2π-periodic function.We prove that if c】0 andμ（θ）≠0,θ∈[0,2π],then eve...In this paper,we deal with the existence of unbounded orbits of the mapping where n is a positive integer,c is a constant andμ（θ）is a 2π-periodic function.We prove that if c】0 andμ（θ）≠0,θ∈[0,2π],then every orbit of the given mapping goes to infinity in the future forρlarge enough;if c【0 andμ（θ）≠0,θ∈[0,2π],then every orbit of the given mapping goes to infinity in the past forρlarge enough.By using this result,we prove that the equation x″+f（x）x′+ax<sup>+</sup>-bx<sup>-</sup>+φ（x）= p（t）has unbounded solutions provided that a,b satisfy 1/a<sup>1/2</sup>+1/b<sup>1/2</sup>=2/n and F（x）（=∫<sub>0</sub><sup>x</sup> f（s）ds）, andφ（x）satisfies some limit conditions.At the same time,we obtain the existence of 2π-periodic solutions of this equation.展开更多
In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian s...In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.展开更多
基金Supported by the Research Foundation of Education Department of Zhejiang Province( 2 0 0 380 4 9)
文摘In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).
文摘In this artical the existence, stability and asymptoticity of periodic solutionfor Abel equation :as well as ones for its special cases are discussed, where a(t), b(t), c(t) and d(t)are real periodic functions.
基金the National Natural Science Foundation of China(Grant No.10471099)the Fund of Beijing Education Committee(Grant No.KM200410028003)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of China
文摘In this paper,we deal with the existence of unbounded orbits of the mapping where n is a positive integer,c is a constant andμ（θ）is a 2π-periodic function.We prove that if c】0 andμ（θ）≠0,θ∈[0,2π],then every orbit of the given mapping goes to infinity in the future forρlarge enough;if c【0 andμ（θ）≠0,θ∈[0,2π],then every orbit of the given mapping goes to infinity in the past forρlarge enough.By using this result,we prove that the equation x″+f（x）x′+ax<sup>+</sup>-bx<sup>-</sup>+φ（x）= p（t）has unbounded solutions provided that a,b satisfy 1/a<sup>1/2</sup>+1/b<sup>1/2</sup>=2/n and F（x）（=∫<sub>0</sub><sup>x</sup> f（s）ds）, andφ（x）satisfies some limit conditions.At the same time,we obtain the existence of 2π-periodic solutions of this equation.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No.20060390014)
文摘In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.
