In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w ...In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w is an integer. This is done using the Banach fixed point theorem. An example involving the heat operator is discussed as an illustration of the theory.展开更多
In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic ...In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.展开更多
In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for osc...In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation.展开更多
The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equatio...The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments.展开更多
In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), wit...In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), with Pm > 0, we establish some new sufficient conditions for an arbitrary solution N(t) to satisfy the initial conditions of the form N(0) = NO > 0 and N(-j) = N-j ≥ 0,j = 1, 2, ., m, to converge to the positive equilibrium N* as t →∞.展开更多
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.
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
For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-al...For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.展开更多
文摘In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w is an integer. This is done using the Banach fixed point theorem. An example involving the heat operator is discussed as an illustration of the theory.
基金Supported by the Science Foundation of Fushun Petroleum Institute
文摘In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271380,11031002 and 11371058)Research Fund for the Doctoral Program of Higher Education(Grant No.20110003110004)+1 种基金the Grant of BeijingEducation Committee Key Project(Grant No.KZ201310028031)Natural Science Foundation of GuangdongProvince of China(Grant No.S2013010013212)
文摘In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.
文摘In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation.
基金Supported partially by the Youthful Sciences Foundation of Shanxi(20021003).
文摘The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments.
基金Supported by the Science Foundation of Hunan Educational Commites (99C12)
文摘In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), with Pm > 0, we establish some new sufficient conditions for an arbitrary solution N(t) to satisfy the initial conditions of the form N(0) = NO > 0 and N(-j) = N-j ≥ 0,j = 1, 2, ., m, to converge to the positive equilibrium N* as t →∞.
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.
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.
文摘For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.
