This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of...This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.展开更多
For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain li...For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.展开更多
In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions i...In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.展开更多
This paper studies the nonautonomous nonlinear system of difference equations △x（n） A（n）x（n） ＋ f（n,x（n））, n∈Z ,（＊）where x（n）∈R^N,A（n） = （aij（n））N×N is an N×N matrix, with aij∈C（R,R...This paper studies the nonautonomous nonlinear system of difference equations △x（n） A（n）x（n） ＋ f（n,x（n））, n∈Z ,（＊）where x（n）∈R^N,A（n） = （aij（n））N×N is an N×N matrix, with aij∈C（R,R） for i,j = 1,2,3 ,N, and f = （f1,f2,... ,fN）^T ∈C（R×R^N,R^N）, satisfying A（t＋） = A（t）, f（t＋ω,z） = f（t, z） for any t∈R, （t, z） ∈R× RN and ∈is a positive integer. Sufficient conditions for the existence of ω-periodic solutions to equations （＊） are obtained.展开更多
In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the f...In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.展开更多
In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions ...In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.展开更多
Let,. We study the existence and multiple positive solutions of n-th nonlinear discrete fractional boundary value problem of the form By using a fixed-point theorem on cone, the parameter intervals of problem is estab...Let,. We study the existence and multiple positive solutions of n-th nonlinear discrete fractional boundary value problem of the form By using a fixed-point theorem on cone, the parameter intervals of problem is established.展开更多
We study the convergence of the positive solutions of the system of the following two difference equations: where K is a positive integer, the parameters?A,B,?α, β? and the initial conditions are positive real numbe...We study the convergence of the positive solutions of the system of the following two difference equations: where K is a positive integer, the parameters?A,B,?α, β? and the initial conditions are positive real numbers. Our results generalize well known results in [1,2].展开更多
The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreas...The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreasing sequence of integers, τ(n)<n and lim n →∞ τ(n) =∞. A sufficient condition for the existence of positive solutions of the equation was given.展开更多
The aim of this paper is to show that the following difference equation：Xn＋1=α＋（xn-k/xn-m）^p, n=0,1,2,…,where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k＋1,…,x-m,…,X-1, x0 are positive, has p...The aim of this paper is to show that the following difference equation：Xn＋1=α＋（xn-k/xn-m）^p, n=0,1,2,…,where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k＋1,…,x-m,…,X-1, x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α＋1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.展开更多
There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response, diffusion, and time delays is investigated. The model consists of n competing preys and one predator, and the predator and ...A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response, diffusion, and time delays is investigated. The model consists of n competing preys and one predator, and the predator and one prey are confined to one patch. First, eon^pts and results concerning the continuation theorem of coincidence degree are summarized. Then, a system of algebraic equations is proved to have a unique solution. Finally, the sufficient conditions for the existence of a difference system are established. The result is substantiated through numerical simulation.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Legg...In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.展开更多
The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-...The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.展开更多
In the present paper, we consider the existence of positive periodic solutions for a kind of delay Logistic equations. By using a fixed point theorem in cones, we give some new existence results of single and multiple...In the present paper, we consider the existence of positive periodic solutions for a kind of delay Logistic equations. By using a fixed point theorem in cones, we give some new existence results of single and multiple positive periodic solutions for a kind of delay Logistic equations. Some biomathematical models are presented to illustrate our results.展开更多
基金Supported by the Natural Science Foundation of Hunan Province（12JJ6006） Supported by the Science Foundation of Department of Science and Technology of Hunan Province（2012FJ3107）
文摘This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.
文摘For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.
基金the National Natural Science Foundation of China(1 0 0 71 0 1 8)
文摘In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.
基金Supported by the NNSF of China(10571050),the EYTP of China and the Science Foundation of the Education Committee of Hunan Province(04C457).
文摘This paper studies the nonautonomous nonlinear system of difference equations △x（n） A（n）x（n） ＋ f（n,x（n））, n∈Z ,（＊）where x（n）∈R^N,A（n） = （aij（n））N×N is an N×N matrix, with aij∈C（R,R） for i,j = 1,2,3 ,N, and f = （f1,f2,... ,fN）^T ∈C（R×R^N,R^N）, satisfying A（t＋） = A（t）, f（t＋ω,z） = f（t, z） for any t∈R, （t, z） ∈R× RN and ∈is a positive integer. Sufficient conditions for the existence of ω-periodic solutions to equations （＊） are obtained.
基金Project(10471153) supported by the National Natural Science Foundation of China project supported by the Natural Science Foundation of Central South University
文摘In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.
文摘In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.
文摘Let,. We study the existence and multiple positive solutions of n-th nonlinear discrete fractional boundary value problem of the form By using a fixed-point theorem on cone, the parameter intervals of problem is established.
文摘We study the convergence of the positive solutions of the system of the following two difference equations: where K is a positive integer, the parameters?A,B,?α, β? and the initial conditions are positive real numbers. Our results generalize well known results in [1,2].
文摘The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreasing sequence of integers, τ(n)<n and lim n →∞ τ(n) =∞. A sufficient condition for the existence of positive solutions of the equation was given.
文摘The aim of this paper is to show that the following difference equation：Xn＋1=α＋（xn-k/xn-m）^p, n=0,1,2,…,where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k＋1,…,x-m,…,X-1, x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α＋1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.
文摘There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
基金The National Natural Science Foundation of China (Nos.60671063,10571113,and 10871122)
文摘A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response, diffusion, and time delays is investigated. The model consists of n competing preys and one predator, and the predator and one prey are confined to one patch. First, eon^pts and results concerning the continuation theorem of coincidence degree are summarized. Then, a system of algebraic equations is proved to have a unique solution. Finally, the sufficient conditions for the existence of a difference system are established. The result is substantiated through numerical simulation.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
文摘In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.
基金The first author was supported by the Science Foundation of Educational Committee of HunanProvince ( 99C0 1 ) and the second author by the National Natural Science Foundation of China ( 1 9871 0 0 5 )
文摘The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.
文摘In the present paper, we consider the existence of positive periodic solutions for a kind of delay Logistic equations. By using a fixed point theorem in cones, we give some new existence results of single and multiple positive periodic solutions for a kind of delay Logistic equations. Some biomathematical models are presented to illustrate our results.
