In this paper, we study the oscillatory and asymptotic behavior of second order neutral delay difference equation with “maxima” of the form? Examples are given to illustrate the main result.
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
The asymptotic behavior of the solutions to a class of second order quasilinear differential equations is considered. The main results improve and generalize those in Elbert and Kusano [3].
The asymptotic behavior of the nonoscillatory solutions of the difference equations △[r(n)△x(n)]+f(n,x(n),x(r(n,x(n))))=0 is considered. In the case when f is a strongly sublinear (superlinear) function, conditions ...The asymptotic behavior of the nonoscillatory solutions of the difference equations △[r(n)△x(n)]+f(n,x(n),x(r(n,x(n))))=0 is considered. In the case when f is a strongly sublinear (superlinear) function, conditions for oscillations of (1) are also found.展开更多
The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)...The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)-x(t_k)=b_kx(t_k). Our results. which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations. improve and generalize the known results recently obtained in [8].展开更多
The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→...The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→∞. Our results improve and extend some corresponding ones already known.展开更多
Sufficient conditions are established for the asymptotic behavior of solutions of nonlinear delay differential equationswhere equipped with the sup norm for some r > 0. A new result is established, some known resul...Sufficient conditions are established for the asymptotic behavior of solutions of nonlinear delay differential equationswhere equipped with the sup norm for some r > 0. A new result is established, some known results are improved.展开更多
The asymptotic behavior and oscillation of the solutions of second order integro-differential equations with deviating argumentis studied. Our technique depends on an integral inequality containing a deviating argumen...The asymptotic behavior and oscillation of the solutions of second order integro-differential equations with deviating argumentis studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1.4) have some asymptotic behavior and oscillation.展开更多
In this paper, we consider the oscillatory and asymptotic behavior of solution of first order nonlinear neutral functional differential equation with piecewise constant dealy. We prove that all solutions of the equati...In this paper, we consider the oscillatory and asymptotic behavior of solution of first order nonlinear neutral functional differential equation with piecewise constant dealy. We prove that all solutions of the equation are nonoscillatory and several criteria for the asymptotic behavior of nonoscillatory solutions of the equation are also obtained.展开更多
Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained ...Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained for all solutions to be oscillatory when the equation is of oscillating coefficients.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
Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The ...Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.展开更多
The asymptotic behavior of solutions to certain integro-differential equation of arbitrary order is studied. Examples are given to illustrate the results.
In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algori...In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algorithm for the singleinterval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy ofthe proposed methods.展开更多
In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic...In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic behavior of solutions is stressed in this paper.At last,we illustrate our results with two examples.展开更多
By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous lit...By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous literatures.展开更多
In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our...In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our results generalize and improve the previous results.展开更多
This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which t...This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.展开更多
文摘In this paper, we study the oscillatory and asymptotic behavior of second order neutral delay difference equation with “maxima” of the form? Examples are given to illustrate the main result.
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.
文摘The asymptotic behavior of the solutions to a class of second order quasilinear differential equations is considered. The main results improve and generalize those in Elbert and Kusano [3].
基金the National Natural Science Foundation of China (No.69982002) and theNationa1 Key Basic Research Special Found (No.G199802030
文摘The asymptotic behavior of the nonoscillatory solutions of the difference equations △[r(n)△x(n)]+f(n,x(n),x(r(n,x(n))))=0 is considered. In the case when f is a strongly sublinear (superlinear) function, conditions for oscillations of (1) are also found.
基金This work is supported by the NNSF of China and the NSF of Hunan Province
文摘The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)-x(t_k)=b_kx(t_k). Our results. which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations. improve and generalize the known results recently obtained in [8].
基金Research supported by the Natural Science Foundation of China(10371034)the Specialized Research Fund for the Doctoral Program of Higher Education(20050532023)
文摘The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→∞. Our results improve and extend some corresponding ones already known.
文摘Sufficient conditions are established for the asymptotic behavior of solutions of nonlinear delay differential equationswhere equipped with the sup norm for some r > 0. A new result is established, some known results are improved.
文摘The asymptotic behavior and oscillation of the solutions of second order integro-differential equations with deviating argumentis studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1.4) have some asymptotic behavior and oscillation.
文摘In this paper, we consider the oscillatory and asymptotic behavior of solution of first order nonlinear neutral functional differential equation with piecewise constant dealy. We prove that all solutions of the equation are nonoscillatory and several criteria for the asymptotic behavior of nonoscillatory solutions of the equation are also obtained.
文摘Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained for all solutions to be oscillatory when the equation is of oscillating coefficients.
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Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.
文摘The asymptotic behavior of solutions to certain integro-differential equation of arbitrary order is studied. Examples are given to illustrate the results.
基金The first author is supported in part by the National Science Foundation of China(Nos.11226330 and 11301343)the Research Fund for the Doctoral Program of Higher Education of China(No.20113127120002)+5 种基金the Research Fund for Young Teachers Program in Shanghai(No.shsf018)and the Fund for E-institute of Shanghai Universities(No.E03004)The second author is supported in part by the National Science Foundation of China(No.11171225)the Research Fund for the Doctoral Program of Higher Education of China(No.20133127110006)the Innovation Program of Shanghai Municipal Education Commission(No.12ZZ131)the Fund for E-institute of Shanghai Universities(No.E03004).
文摘In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algorithm for the singleinterval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy ofthe proposed methods.
基金supported by the National Natural Science Foundation of China(No.10971231)the NSF of Guangdong Province (No.8151027501000053)Project of Zhongkai University Agriculture and Engineering (G3071728)
文摘In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic behavior of solutions is stressed in this paper.At last,we illustrate our results with two examples.
文摘By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous literatures.
文摘In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our results generalize and improve the previous results.
基金The work of this author is supported in part by E-Institutes of Shanghai Municipal Education Commission （No. E03004）, Shanghai Science and Technology Commission （No.03QA14036）, Shanghai Leading Academic Discipline Project （No. T0401）, Science Foundation of Shanghai （No. 04JC14062） and Special Funds for Major Specialties of Shanghai Education Commission.Acknowledgement. The authors wish to thank the anonymous referees for their carefully correcting the preliminary version of the manuscript.
文摘This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.
