By means of continuation theorem of the coincidence degree theory, sufficient conditions are obtained for the existence of periodic solutions of a kind of third-order neutral delay functional differential equation wit...By means of continuation theorem of the coincidence degree theory, sufficient conditions are obtained for the existence of periodic solutions of a kind of third-order neutral delay functional differential equation with deviating arguments.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
In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational c...In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.展开更多
By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalizat...By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.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
A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive...A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.展开更多
In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization an...In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.展开更多
This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which ...This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which will be stated later.The periodicity problem has been one of main topics in the qualitative theory of ordinary展开更多
This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment ...This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.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
The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.
The problem of periodic solutions for a kind of kth-order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the ex...The problem of periodic solutions for a kind of kth-order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the existence and uniqueness of periodic solution is obtained. Further, by applying this result and Schauder's fixed point principle, a kind of kth-order nonlinear neutral functional differential equation is investigated, and some new results on existence of the periodic solutions are given as well. These results improve and extend some known results in recent literature.展开更多
Using piecewise constant orthonormal functions, an approximation of the monodromy operator of a Linear Periodic Delay Differential Equation (PDDE) is obtained by approximating the integral equation corresponding to th...Using piecewise constant orthonormal functions, an approximation of the monodromy operator of a Linear Periodic Delay Differential Equation (PDDE) is obtained by approximating the integral equation corresponding to the PDDE as a linear operator over the space of initial conditions. This approximation allows us to consider the state space as finite dimensional resulting in a finite matrix approximation whose spectrum converges to the spectrum of the monodromy operator.展开更多
This paper deals with a class of <em>n</em>-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (<em>n</em> is an odd...This paper deals with a class of <em>n</em>-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (<em>n</em> is an odd number) or two (<em>n</em> is an even number) periodic solutions of the equation is obtained. These conclusions have certain application value for judging the existence of periodic solutions of polynomial differential equations with only one higher-order term.展开更多
nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.
Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples ...Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples to demonstrate our results.展开更多
This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions wh...This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.展开更多
In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results ...In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.展开更多
文摘By means of continuation theorem of the coincidence degree theory, sufficient conditions are obtained for the existence of periodic solutions of a kind of third-order neutral delay functional differential equation with deviating arguments.
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.
文摘In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.
基金The second author partially supported by NSFC (10571179, 10871203) GrantProgramfor New Century Excellent Talents in University of Ministry of Eduction of China
文摘By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.
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))].
文摘A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.
基金supported by the National Natural Science Foundation of China(11371027) the Projects of Outstanding Young Talents of Universities in Anhui Province(gxyq2018116)+2 种基金 the Teaching Groups in Anhui Province(2016jxtd080,2015jxtd048) the NSF of Educational Bureau of Anhui Province(KJ2017A702,KJ2017A704) the NSF of Bozhou University(BZSZKYXM201302,BSKY201539)
文摘In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
基金National Natural Science Foundation of China(No.10971139)Fundamental Research Funds for the Central Universities,China(No.B081)
文摘In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.
文摘This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which will be stated later.The periodicity problem has been one of main topics in the qualitative theory of ordinary
文摘This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.
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.
基金theAppliedScienceFoundationofYunnan China (97A10 16Q)
文摘The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.
文摘The problem of periodic solutions for a kind of kth-order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the existence and uniqueness of periodic solution is obtained. Further, by applying this result and Schauder's fixed point principle, a kind of kth-order nonlinear neutral functional differential equation is investigated, and some new results on existence of the periodic solutions are given as well. These results improve and extend some known results in recent literature.
文摘Using piecewise constant orthonormal functions, an approximation of the monodromy operator of a Linear Periodic Delay Differential Equation (PDDE) is obtained by approximating the integral equation corresponding to the PDDE as a linear operator over the space of initial conditions. This approximation allows us to consider the state space as finite dimensional resulting in a finite matrix approximation whose spectrum converges to the spectrum of the monodromy operator.
文摘This paper deals with a class of <em>n</em>-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (<em>n</em> is an odd number) or two (<em>n</em> is an even number) periodic solutions of the equation is obtained. These conclusions have certain application value for judging the existence of periodic solutions of polynomial differential equations with only one higher-order term.
文摘nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.
基金Supported by Postdoctoral Science Foundation of China (No.200114).
文摘Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples to demonstrate our results.
文摘This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.
基金Supported by the Natural Science Foundation of Anhui Province(2004KJ028).
文摘In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.