Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic sol...Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.展开更多
In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a ge...In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of solutions.展开更多
This paper considers a class of fourth order nonlinear difference equations Δ<sup>2</sup>（r<sub>n</sub>Δ<sup>2</sup>y<sub>n</sub>）+ f（n,y<sub>n</sub>）=...This paper considers a class of fourth order nonlinear difference equations Δ<sup>2</sup>（r<sub>n</sub>Δ<sup>2</sup>y<sub>n</sub>）+ f（n,y<sub>n</sub>）=0,n∈N（n<sub>0</sub>）,where f（n,y）may be classified as superlinear,sublinear,strongly super- linear and strongly sublinear.In superlinear and sublinear cases,necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties.In strongly superlinear and strongly sublinear cases,sufficient conditions are given for all solutions to be oscillatory.展开更多
The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonline...The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included.展开更多
In this paper, a class of nonlinear difference equations are investigated. The sufficient conditions for the nonexistence of positive solutions are obtained. The results in this paper improve ones in [2].
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., ...In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.展开更多
We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we pro...We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we propose a rule for a time-stepping,which is a variant of what was successfully used in the case of nonlinear parabolic equations. A numerical blow-up time is defined and is proved to converge, under a certain hypothesis, to the real blow-up time as the grid size tends to zero.展开更多
Consider the second order nonlinear neutral difference equationThe sufficient conditions are established for the oscillation and asymptotic behavior of the solutions of this equation.
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
Sufficient conditions to guarantee all solutions to be oscillatory of a second order nonlinear impulsive difference equation are obtained by using Riccati transformation.
By using Banach contraction principle, we obtain the global results （with respect to ｜｜A｜｜≠1） on the sufficient conditions for the existence of nonoscillatory solutions to a system of nonlinear neutral delay di...By using Banach contraction principle, we obtain the global results （with respect to ｜｜A｜｜≠1） on the sufficient conditions for the existence of nonoscillatory solutions to a system of nonlinear neutral delay difference equations with matrix coefficients.展开更多
In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
In this paper, we apply a critical point theorem and obtain the condition for the existence of three solutions to two-point boundary value problem of a second order nonlinear difference equation.
We study the periodicity of the positive solutions of a class of difference equations with maximum. We prove that every positive solutions of these equations are eventually periodic.
In this paper,two different n-order topological circuit networks are connected by diodes to establish a unified network model,which is a previously unexplored problem.The network model includes not only five resistive...In this paper,two different n-order topological circuit networks are connected by diodes to establish a unified network model,which is a previously unexplored problem.The network model includes not only five resistive elements but also diode devices,so the network contains many different network types.This problem can be solved through three main steps:First,the network is simplified into two different equivalent circuit models.Second,the nonlinear difference equation model is established by applying Kirchhoff’s law.Finally,the two equations with similar structures are processed uniformly,and the general solutions of the nonlinear difference equations are obtained by using the transformation technique.As an example,several interesting specific results are deduced.Our study on the network model has significant value,as it can be applied to relevant interdisciplinary research.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10871076)
文摘Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.
基金Supported by Program for Changjiang Scholars and Innovative Research Team in University (Grant No.IRT1226)National Natural Science Foundation of China (Grant Nos. 11171078 and 11031002)the Specialized Fund for the Doctoral Program of Higher Education of China (Grant No. 20114410110002)
文摘In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of solutions.
基金Partially Supported by the National Science Foundation of China
文摘This paper considers a class of fourth order nonlinear difference equations Δ<sup>2</sup>（r<sub>n</sub>Δ<sup>2</sup>y<sub>n</sub>）+ f（n,y<sub>n</sub>）=0,n∈N（n<sub>0</sub>）,where f（n,y）may be classified as superlinear,sublinear,strongly super- linear and strongly sublinear.In superlinear and sublinear cases,necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties.In strongly superlinear and strongly sublinear cases,sufficient conditions are given for all solutions to be oscillatory.
基金Foundation items: the National Natural Science Foundation of China (10171040)the Natural Science Foundation of Gansu Province of China (ZS011-A25-007-Z)+1 种基金 the Foundation for University Key Teacher by Ministry of Education of China the Teaching and Re
文摘The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included.
文摘In this paper, a class of nonlinear difference equations are investigated. The sufficient conditions for the nonexistence of positive solutions are obtained. The results in this paper improve ones in [2].
基金Supported by the National Natural Science Foundation of China(1 0 0 71 0 2 2 ) Mathematical TianyuanFoundation of China(TY1 0 0 2 6 0 0 2 - 0 1 - 0 5 - 0 3 ) Shanghai Priority Academic Discipline Foundation
文摘In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.
基金supported by the grant NSC 98-2115-M-194-010-MY2
文摘We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we propose a rule for a time-stepping,which is a variant of what was successfully used in the case of nonlinear parabolic equations. A numerical blow-up time is defined and is proved to converge, under a certain hypothesis, to the real blow-up time as the grid size tends to zero.
文摘Consider the second order nonlinear neutral difference equationThe sufficient conditions are established for the oscillation and asymptotic behavior of the solutions of this equation.
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Partially supported by Guangdong Natural Science Foundation (980018).
文摘Sufficient conditions to guarantee all solutions to be oscillatory of a second order nonlinear impulsive difference equation are obtained by using Riccati transformation.
基金This work is supported by the National Natural Sciences Foundation of China under Grant 10361006the Natural Sciences Foundation of Yunnan Province under Grant 2003A0001MYouth Natural Sciences Foundation of Yunnan University under Grant 2003Q032C and Sciences Foundation of Yunnan Educational Community under Grant 04Y239A.
文摘By using Banach contraction principle, we obtain the global results （with respect to ｜｜A｜｜≠1） on the sufficient conditions for the existence of nonoscillatory solutions to a system of nonlinear neutral delay difference equations with matrix coefficients.
文摘In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
文摘In this paper, we apply a critical point theorem and obtain the condition for the existence of three solutions to two-point boundary value problem of a second order nonlinear difference equation.
文摘We study the periodicity of the positive solutions of a class of difference equations with maximum. We prove that every positive solutions of these equations are eventually periodic.
文摘In this paper,two different n-order topological circuit networks are connected by diodes to establish a unified network model,which is a previously unexplored problem.The network model includes not only five resistive elements but also diode devices,so the network contains many different network types.This problem can be solved through three main steps:First,the network is simplified into two different equivalent circuit models.Second,the nonlinear difference equation model is established by applying Kirchhoff’s law.Finally,the two equations with similar structures are processed uniformly,and the general solutions of the nonlinear difference equations are obtained by using the transformation technique.As an example,several interesting specific results are deduced.Our study on the network model has significant value,as it can be applied to relevant interdisciplinary research.
