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 higher order neutral difference equations is considered and some sufficient conditions are obtained for all solutions to oscillate or tend to zero.
The initial-boundary value problem for a class of nonlinear hyperbolic equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obta...The initial-boundary value problem for a class of nonlinear hyperbolic equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the asymptotic stability of global solutions by means of a difference inequality.展开更多
In this paper, we investigate the asymptotic behavior of the following quasilinear difference equations (E) where , . We classified the solutions into six types by means of their asymptotic behavior. We establish the ...In this paper, we investigate the asymptotic behavior of the following quasilinear difference equations (E) where , . We classified the solutions into six types by means of their asymptotic behavior. We establish the necessary and/or sufficient conditions for such equations to possess a solution of each of these six types.展开更多
J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate...J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.展开更多
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
In this paper, we consider the neutral difference equation△(x n-cx n-m )+p nx n-k =0, n=N, N+1, N+2, …,where c and p n are real numbers, k, m are positive integers with m<k, and △ den...In this paper, we consider the neutral difference equation△(x n-cx n-m )+p nx n-k =0, n=N, N+1, N+2, …,where c and p n are real numbers, k, m are positive integers with m<k, and △ denotes the forward difference operator: △ u n=u n+1 -u n. By using the Krasnoselskii fixed theorem, we obtain some sufficient conditions under which such an equation has a bounded and eventually positive solution which tends to zero as n→∞.展开更多
This paper is concerned with the study of asymptotic behavior of nonoscillatory solutions of second order neutral nonlinear difference equations of theformwhere λ∈ {-1,1},△ is the forword difference operator define...This paper is concerned with the study of asymptotic behavior of nonoscillatory solutions of second order neutral nonlinear difference equations of theformwhere λ∈ {-1,1},△ is the forword difference operator defined by △x_n=x_n+1 x+n.展开更多
In this paper, we investigate the asymptotic behavior of the extremal solutions of a difference equation and their character and prove the existence of the non-extremal solutions.
In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the soluti...In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the solutions to the equation are some high order of infinities,and also that some conditions which guarantee that every oscillatory solution to the equation has the property that the i order L operator of it tends to infinity when its independent variable tends to zero.展开更多
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
A class of neutral type higher order difference equations is considered. Some sufficient conditions of oscillation and asymptotic behavior of solutions is given.
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions ...The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.展开更多
In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form{xn＋1=αnxn＋bnf（yn）,yn=cnyn-1＋dng（xn）.We＇ classify their soluti...In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form{xn＋1=αnxn＋bnf（yn）,yn=cnyn-1＋dng（xn）.We＇ classify their solutions according to asymptotic behavior and give some sufficient and necessary conditions for the existence of solutions of such classes by using the method of the fixed point theorem. We also give an example and show how the results can be applied to certain difference systems.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 higher order neutral difference equations is considered and some sufficient conditions are obtained for all solutions to oscillate or tend to zero.
基金supported by National Natural Science Foundation of China(61273016)The Natural Science Foundation of Zhejiang Province(Y6100016)The Public Welfare Technology Application Research Project of Zhejiang Province Science and Technology Department(2015C33088)
文摘The initial-boundary value problem for a class of nonlinear hyperbolic equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the asymptotic stability of global solutions by means of a difference inequality.
文摘In this paper, we investigate the asymptotic behavior of the following quasilinear difference equations (E) where , . We classified the solutions into six types by means of their asymptotic behavior. We establish the necessary and/or sufficient conditions for such equations to possess a solution of each of these six types.
文摘J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.
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In this paper, we consider the neutral difference equation△(x n-cx n-m )+p nx n-k =0, n=N, N+1, N+2, …,where c and p n are real numbers, k, m are positive integers with m<k, and △ denotes the forward difference operator: △ u n=u n+1 -u n. By using the Krasnoselskii fixed theorem, we obtain some sufficient conditions under which such an equation has a bounded and eventually positive solution which tends to zero as n→∞.
文摘This paper is concerned with the study of asymptotic behavior of nonoscillatory solutions of second order neutral nonlinear difference equations of theformwhere λ∈ {-1,1},△ is the forword difference operator defined by △x_n=x_n+1 x+n.
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute.
文摘In this paper, we investigate the asymptotic behavior of the extremal solutions of a difference equation and their character and prove the existence of the non-extremal solutions.
文摘In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the solutions to the equation are some high order of infinities,and also that some conditions which guarantee that every oscillatory solution to the equation has the property that the i order L operator of it tends to infinity when its independent variable tends to zero.
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.
文摘A class of neutral type higher order difference equations is considered. Some sufficient conditions of oscillation and asymptotic behavior of solutions is given.
基金Project supported by Natural Science Foundation of Guangdong (011471)Foundation for the study of Natural Science for Universities of Guangdong (0120).
文摘The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.
文摘In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form{xn＋1=αnxn＋bnf（yn）,yn=cnyn-1＋dng（xn）.We＇ classify their solutions according to asymptotic behavior and give some sufficient and necessary conditions for the existence of solutions of such classes by using the method of the fixed point theorem. We also give an example and show how the results can be applied to certain difference systems.
