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
This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is p...This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is provided. One examplefrom practicc electrical network problem is used to test all these theory.展开更多
In this paper, the existence and uniqueness of periodic solutions of linearfunctional differential equat,ions, including neutral equations, with constant coef-ficients are investigated, necessary and sufficient condit...In this paper, the existence and uniqueness of periodic solutions of linearfunctional differential equat,ions, including neutral equations, with constant coef-ficients are investigated, necessary and sufficient conditions for the existence anduniqueness of periodic solutions of linear neutral functional differential equationsand some of their special oases are given via systems of linear algebraic equations. Especially, the problems of existonce and Uniqueness of periodic solutions ofgeneral linear functional differential equations of non-neutral type are completelysolved.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.
By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vec...By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vector. We show that if the Melnikov-type vector satisfies some conditions then autonomous differential equations have homoclinic solutions. Moreover, our result holds only for autonomous differential equations.展开更多
Consider the general sublinear ordinary differential equations of second order of theform X(t) + a(t)f(X(t)) =0, where a(t)∈C[t0,∞),f(x)∈C(R)and xf(x)>0,f'(x) ≥ 0 for x ≠ 0.Furthermore,f(x) also satisfies ...Consider the general sublinear ordinary differential equations of second order of theform X(t) + a(t)f(X(t)) =0, where a(t)∈C[t0,∞),f(x)∈C(R)and xf(x)>0,f'(x) ≥ 0 for x ≠ 0.Furthermore,f(x) also satisfies sublinear condition, which coversthe prototype nonlinear function f(x)=|x|γ sgnx with 0<γ<1 known as the EmdenFowler case. The coefficient α(t) is not assumed to be eventually nonnegative. A new oscillation criterion involving integral averages of α(t) due to Kamenev (Math. Zametki 23(1978), 249 - 251 ) for linear equation and Wong (Conference Proceedings, Canad. Math.Soc. 8(1987), 299-302) for Emder-Fowler equation with 0<γ<1 is shown to remainvalid for general sublinear equation.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This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is provided. One examplefrom practicc electrical network problem is used to test all these theory.
文摘In this paper, the existence and uniqueness of periodic solutions of linearfunctional differential equat,ions, including neutral equations, with constant coef-ficients are investigated, necessary and sufficient conditions for the existence anduniqueness of periodic solutions of linear neutral functional differential equationsand some of their special oases are given via systems of linear algebraic equations. Especially, the problems of existonce and Uniqueness of periodic solutions ofgeneral linear functional differential equations of non-neutral type are completelysolved.
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.
文摘By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vector. We show that if the Melnikov-type vector satisfies some conditions then autonomous differential equations have homoclinic solutions. Moreover, our result holds only for autonomous differential equations.
文摘Consider the general sublinear ordinary differential equations of second order of theform X(t) + a(t)f(X(t)) =0, where a(t)∈C[t0,∞),f(x)∈C(R)and xf(x)>0,f'(x) ≥ 0 for x ≠ 0.Furthermore,f(x) also satisfies sublinear condition, which coversthe prototype nonlinear function f(x)=|x|γ sgnx with 0<γ<1 known as the EmdenFowler case. The coefficient α(t) is not assumed to be eventually nonnegative. A new oscillation criterion involving integral averages of α(t) due to Kamenev (Math. Zametki 23(1978), 249 - 251 ) for linear equation and Wong (Conference Proceedings, Canad. Math.Soc. 8(1987), 299-302) for Emder-Fowler equation with 0<γ<1 is shown to remainvalid for general sublinear equation.
