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
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
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
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
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.
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, 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 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
The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1...The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions展开更多
We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our ...We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our approach is based on the continuation theorem of coincidence degree, andthe α-priori: estimate of periodic solutions.展开更多
By means of an extension of Mawhin＇s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, ...By means of an extension of Mawhin＇s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.展开更多
We obtain sufficient conditions for the existence of periodic solutions ofthe following second order nonlinear differential equation: ax(t) + bx^(2k-1)(t) + cx^(2k-1)9t) +g(x(t - τ_1), x(t - τ_2)) = p(t) = p(t + 2π...We obtain sufficient conditions for the existence of periodic solutions ofthe following second order nonlinear differential equation: ax(t) + bx^(2k-1)(t) + cx^(2k-1)9t) +g(x(t - τ_1), x(t - τ_2)) = p(t) = p(t + 2π). Our approach is based on the continuation theoremof the coincidence degree, and the priori estimate of periodic solutions.展开更多
Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with ...Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.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.
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 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.
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.
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 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.
基金Supported by the National Natural Science Foundation of China(1 9971 0 2 6 )
文摘The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions
基金The project is supported by NNSF of China(No.10271044)
文摘We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our approach is based on the continuation theorem of coincidence degree, andthe α-priori: estimate of periodic solutions.
基金sponsored by the National Natural Science Foundation of China(11271197)the Science and Technology Foundation in Ministry of Education of China(207047)the Science Foundation of NUIST of China(20090202 and 2012r101)
文摘By means of an extension of Mawhin＇s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.
文摘We obtain sufficient conditions for the existence of periodic solutions ofthe following second order nonlinear differential equation: ax(t) + bx^(2k-1)(t) + cx^(2k-1)9t) +g(x(t - τ_1), x(t - τ_2)) = p(t) = p(t + 2π). Our approach is based on the continuation theoremof the coincidence degree, and the priori estimate of periodic solutions.
基金Supported by Ministry of Education of Science and Technology of Important Projects(207047)Natural Science Foundation of Anhui Province of China(050460103)Key Natural Science Foundation by the Bureau of Education of Anhui Province in China(2005kj031ZD)
基金Supported by the National Natural Science Foundation of China(11071001)Supported by the NSF of Education Bureau of Anhui Province(KJ2009A005Z,KJ2010ZD02,2010SQRL159)+1 种基金Supported by the 211 Project of Anhui University(KJTD002B)Supported by the Natural Science Foundation of Anhui Province(1208085MA13)
文摘Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.
