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
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s...The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.展开更多
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
Based on the inherence theorem to the operator D(t) in [9], we investigate the stability with respect to the hull and the existence on almost periodic solutions for neutral functional differential equations (NFDE). Fo...Based on the inherence theorem to the operator D(t) in [9], we investigate the stability with respect to the hull and the existence on almost periodic solutions for neutral functional differential equations (NFDE). For periodic Eq. (1), we prove that if Eq. (1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to H.f(ξ),then Eq. (1 ) has an mω -- periodic solution p(t), for some integer m ≥1. Furthermore, we prove that if almost periodic Eq. (1 ) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq. (1) has an almost periodic solution.展开更多
By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that s...By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.展开更多
In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence o...In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.展开更多
By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following n...By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation展开更多
Thc main aim of this paper is to use the continuation theorem of coincidence degree theory for studying the existence of periodic solutions to a kind of neutral functional differential equation as follows:(x(t)-^n...Thc main aim of this paper is to use the continuation theorem of coincidence degree theory for studying the existence of periodic solutions to a kind of neutral functional differential equation as follows:(x(t)-^n∑i=1cix(t-ri))″=f(x(t))x′+g(x(t-τ))+p(t).In order to do so, we analyze the structure of the linear difference operator A : C2π→C2π, [Ax](t) =x(t)-∑^ni=1cix(t-ri)to determine some flmdamental properties first, which we are going to use throughout this paper. Meanwhile, we also prove some new inequalities which are useful for estimating a priori bounds of periodie solutions.展开更多
In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays o...In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form (x(t)+Bx(t-δ))"+Cx'(t)+g(x(t-τ))=p(t).展开更多
In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible ...In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.展开更多
In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows:(x(t) - cx(t -τ)" = g(t, x(t - μ(t))) + e(t),in the cr...In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows:(x(t) - cx(t -τ)" = g(t, x(t - μ(t))) + e(t),in the critical case |c| = 1. By employing Mawhin's continuation theorem and some analysis techniques, some new results are obtained.展开更多
By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.
In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uni...In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uniqueness of the periodic solution are obtained.展开更多
For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if perio...For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.展开更多
We obtain sufficient conditions for class of second order neutral functional theorem of the coincidence degree. the existence of periodic solution to a differential equation, using continuation
A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis th...A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.展开更多
In this paper, we investigate a third-order generalized neutral functional differential equation with variable parameter. Based on Mawhin’s coincidence degree theory and some analysis skills, we obtain sufficient con...In this paper, we investigate a third-order generalized neutral functional differential equation with variable parameter. Based on Mawhin’s coincidence degree theory and some analysis skills, we obtain sufficient conditions for the existence of periodic solution for the equation. An example is also provided.展开更多
We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii’s fixed-point theorem, some results about the existence of positive periodic so...We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii’s fixed-point theorem, some results about the existence of positive periodic solution to the systems are obtained, which complement the previous known results.展开更多
By using the generalized degree theory, some periodically perturbed functional differential equations have been proved to have at least one periodic solution if the associated homogeneous linear equations have no nont...By using the generalized degree theory, some periodically perturbed functional differential equations have been proved to have at least one periodic solution if the associated homogeneous linear equations have no nontrivial periodic solution. Some known results are generalized.展开更多
By means of Mawhin's continuation theorem and some analysis methods, the existence of 2kT-periodic solutions is studied for a class of neutral functional differential equations, and then a homoclinic solution is obta...By means of Mawhin's continuation theorem and some analysis methods, the existence of 2kT-periodic solutions is studied for a class of neutral functional differential equations, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above periodic solutions set.展开更多
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The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
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Based on the inherence theorem to the operator D(t) in [9], we investigate the stability with respect to the hull and the existence on almost periodic solutions for neutral functional differential equations (NFDE). For periodic Eq. (1), we prove that if Eq. (1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to H.f(ξ),then Eq. (1 ) has an mω -- periodic solution p(t), for some integer m ≥1. Furthermore, we prove that if almost periodic Eq. (1 ) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq. (1) has an almost periodic solution.
基金supported by Natural Science Foundation of Education Department of Anhui Province (No.KJ2010B353)Young Teacher’s Foundation of Anhui Normal University (No.2008xqn46)
文摘By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.
文摘In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.
基金Supported by the National Natural Science Foundation of China (No.19871005).
文摘By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation
基金the National Natured Science Foundation (No.10371006)the Natural Science Foundation of Anhui Province of China (2005 kj031ZI):050460103)
文摘Thc main aim of this paper is to use the continuation theorem of coincidence degree theory for studying the existence of periodic solutions to a kind of neutral functional differential equation as follows:(x(t)-^n∑i=1cix(t-ri))″=f(x(t))x′+g(x(t-τ))+p(t).In order to do so, we analyze the structure of the linear difference operator A : C2π→C2π, [Ax](t) =x(t)-∑^ni=1cix(t-ri)to determine some flmdamental properties first, which we are going to use throughout this paper. Meanwhile, we also prove some new inequalities which are useful for estimating a priori bounds of periodie solutions.
基金Supported by the National Natural Science Foundation of China(No.10371034)the Hunan Provincial Natural Science Foundation of China(05JJ40009).
文摘In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form (x(t)+Bx(t-δ))"+Cx'(t)+g(x(t-τ))=p(t).
文摘In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.
基金Supported by the National Natural Science Foundation(1987100510371006)+1 种基金the Natural Science Foundation of Auhui Province of China(0504601032005kj301ZD)
文摘In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows:(x(t) - cx(t -τ)" = g(t, x(t - μ(t))) + e(t),in the critical case |c| = 1. By employing Mawhin's continuation theorem and some analysis techniques, some new results are obtained.
基金supported by the National Natural Science Foundation of China(No10771001)the Key Program of Ministry of Education of China (No205068)the Programof Innovation Team of University of Anhui
文摘By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.
基金Supported by the Science Foundation for the Excellent Youth Scholars of Anhui Province (2010SQRL159)
文摘In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uniqueness of the periodic solution are obtained.
文摘For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.
基金Supported by the Education Department of Anhui Natural Science Foundation (2004kj0282006KJ245B).
文摘We obtain sufficient conditions for class of second order neutral functional theorem of the coincidence degree. the existence of periodic solution to a differential equation, using continuation
基金by the National Natural Science Foundation of China(Nos.11871162,11661050,11561059).
文摘A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.
文摘In this paper, we investigate a third-order generalized neutral functional differential equation with variable parameter. Based on Mawhin’s coincidence degree theory and some analysis skills, we obtain sufficient conditions for the existence of periodic solution for the equation. An example is also provided.
基金sponsored by the National Natural Science Foundation of China (10771001)the NSF of Education Bureau of Anhui Province (KJ2009A005Z+2 种基金 KJ2010ZD02 2010SQRL159)the NSF of Anhui Province (090416237)
文摘We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii’s fixed-point theorem, some results about the existence of positive periodic solution to the systems are obtained, which complement the previous known results.
文摘By using the generalized degree theory, some periodically perturbed functional differential equations have been proved to have at least one periodic solution if the associated homogeneous linear equations have no nontrivial periodic solution. Some known results are generalized.
基金Supported by the key NSF of Education Ministry of China (Grant No. 207047)
文摘By means of Mawhin's continuation theorem and some analysis methods, the existence of 2kT-periodic solutions is studied for a class of neutral functional differential equations, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above periodic solutions set.