Based on the properties on almost periodic sequence, it is proved that the almost periodic solutions for a class of neutral differential equations with piecewise constant argument exist.
By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(...By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(x(t) + px(t - 1)) = qr\left( {2\left[ {\frac{{t + 1}}{2}} \right]} \right) + g{\bf{ }}(t,x(t),x([t]))$$ is studied.展开更多
In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equ...In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.展开更多
Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In addition, the stab...Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In addition, the stability properties of these solutions are characterized by the construction of manifolds of initial data.展开更多
In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples ar...In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.展开更多
A new class of ergodic sequences, pseudo almost periodic sequence, is introduced, and the existence of pseudo almost periodic sequence to difference equation is studied. Based on these, we investigate the existence of...A new class of ergodic sequences, pseudo almost periodic sequence, is introduced, and the existence of pseudo almost periodic sequence to difference equation is studied. Based on these, we investigate the existence of pseudo almost periodic solutions for a nonautonomous, singularly perturbed differential equations with piecewise constant argument.展开更多
We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delay-differential equations with piecewise constant.
In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference equations.On the basis of these,we investigate the...In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference equations.On the basis of these,we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, d/(dt)(y(t)+py(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])).展开更多
基金Project supported by the Postdoctoral Foundation of China.
文摘Based on the properties on almost periodic sequence, it is proved that the almost periodic solutions for a class of neutral differential equations with piecewise constant argument exist.
文摘By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(x(t) + px(t - 1)) = qr\left( {2\left[ {\frac{{t + 1}}{2}} \right]} \right) + g{\bf{ }}(t,x(t),x([t]))$$ is studied.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271380and11031002)Research Fund for the Doctoral Program of Higher Education(Grant No.20110003110004)Natural Science Foundation of Guangdong Province of China(Grant No.10151601501000003)
文摘In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.
基金the National Natural Science Foundation of China(10371010)SRFDP(20030027011)
文摘Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In addition, the stability properties of these solutions are characterized by the construction of manifolds of initial data.
基金The first author is supported by NPU Foundation for Fundamental Research （NPU-FFR-JC20100220） the second author is supported by National Natural Science Foundation （Grant No. 11031002） and RFDP the third author is supported by National Natural Science Foundation （Grant No. 11071048 ）
文摘In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.
基金This work was partially supported by the National Natural Science Foundationof China (Grant No. 19831030) SRF for ROCS, SEM, the Foundation for University Key Teacher by the Ministry of Education National Key Basic Research Special Foundation of Ch
文摘A new class of ergodic sequences, pseudo almost periodic sequence, is introduced, and the existence of pseudo almost periodic sequence to difference equation is studied. Based on these, we investigate the existence of pseudo almost periodic solutions for a nonautonomous, singularly perturbed differential equations with piecewise constant argument.
基金supported by NNSF of China (No.11271380)NSF of Guangdong Province (1015160150100003)Foundation for Distinguished Young Talents in Higher Education of Guangdong of China (No.LYM08014)
文摘We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delay-differential equations with piecewise constant.
文摘In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference equations.On the basis of these,we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, d/(dt)(y(t)+py(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])).
