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Sui Sun Cheng - One of the best experts on this subject based on the ideXlab platform.
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Frequent oscillation in a nonlinear Partial Difference Equation
Central European Journal of Mathematics, 2007Co-Authors: Jun Yang, Yu Jing Zhang, Sui Sun ChengAbstract:This paper is concerned with a class of nonlinear delay Partial Difference Equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these Partial Difference Equations is discussed by employing frequency measures.
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Unsaturated solutions for Partial Difference Equations with forcing terms
Central European Journal of Mathematics, 2006Co-Authors: Zhi-qiang Zhu, Sui Sun ChengAbstract:The concept of unsaturated infinite double sequence is introduced by making use of frequency measures. Unsaturated solutions are then studied for a Partial Difference Equation. Conditions for all solutions to be unsaturated are obtained. Since unsaturated solutions are oscillatory, our results yield oscillation criteria.
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Sturman Theorems for a Partial Difference Equation
Functional differential equations, 2004Co-Authors: Yu. Domshlak, Sui Sun ChengAbstract:This paper is concerned with a class of Partial Difference Equations defined on cylinders of the lattice plane. By means of a major ant pair, we first establish a Sturm type comparison theorem for these Equations on rectangles. Then by the method of separation of variables, we are able to locate an oscillating majorant pair and derive an oscillation criterion for our Partial Difference Equations on cylinders.
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Existence of Monotone Positive Solution of Neutral Partial Difference Equation
Journal of Mathematical Analysis and Applications, 2000Co-Authors: Shutang Liu, Jun Yang, Yong-qing Liu, Xin-ping Guan, Sui Sun ChengAbstract:Abstract This paper is concerned with a class of neutral Partial Difference Equations. The conditions for the existence of monotone eventually positive solutions are established which improve and extend some of the criteria existing in the literature. Comparison theorems are also derived. Results are obtained on the existence of a monotone eventually positive solution of dual Equation.
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General solutions of a three-level Partial Difference Equation
Computers & Mathematics with Applications, 1999Co-Authors: Sui Sun ChengAbstract:Abstract This paper is concerned with a linear Partial Difference Equation which includes the well-known DuFort Frankel multilevel Difference scheme for the heat Equation. By introducing Green's functions for this Equation, we obtain, via a novel formal approach, an explicit formula for all its solutions. Given exponential initial conditions, separable solutions are also found. As applications, we derive several stability criteria for the solutions of this Equation.
Jun Yang - One of the best experts on this subject based on the ideXlab platform.
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Frequent oscillatory criteria for a neutral Partial Difference Equation
2011 International Conference on Multimedia Technology, 2011Co-Authors: Wenzhi Wang, Jun YangAbstract:In this paper, frequent oscillatory criteria of a neutral Partial Difference Equation is studied. By making use of frequency measures, some oscillatory criteria are established and an example is given to illustrate our main result.
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Frequent oscillatory solutions of a neutral Partial Difference Equation with variable delay
2011 International Conference on Multimedia Technology, 2011Co-Authors: Fangfang Jiang, Jun YangAbstract:This paper is concerned with a class of neutral Partial Difference Equations with variable delay. By making use of frequency measures, some new oscillatory criteria are established. And an example is considered to illustrate our main results.
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Frequent oscillatory solutions of a nonlinear Partial Difference Equation
Journal of Computational and Applied Mathematics, 2009Co-Authors: Jun Yang, Yu Jing ZhangAbstract:This paper is concerned with a class of nonlinear delay Partial Difference Equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established.
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Frequent oscillation in a nonlinear Partial Difference Equation
Central European Journal of Mathematics, 2007Co-Authors: Jun Yang, Yu Jing Zhang, Sui Sun ChengAbstract:This paper is concerned with a class of nonlinear delay Partial Difference Equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these Partial Difference Equations is discussed by employing frequency measures.
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Existence of Monotone Positive Solution of Neutral Partial Difference Equation
Journal of Mathematical Analysis and Applications, 2000Co-Authors: Shutang Liu, Jun Yang, Yong-qing Liu, Xin-ping Guan, Sui Sun ChengAbstract:Abstract This paper is concerned with a class of neutral Partial Difference Equations. The conditions for the existence of monotone eventually positive solutions are established which improve and extend some of the criteria existing in the literature. Comparison theorems are also derived. Results are obtained on the existence of a monotone eventually positive solution of dual Equation.
Shin Min Kang - One of the best experts on this subject based on the ideXlab platform.
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uncountably many bounded positive solutions for a second order nonlinear neutral delay Partial Difference Equation
Bulletin of The Iranian Mathematical Society, 2015Co-Authors: Z Liu, J S Ume, Shin Min KangAbstract:In this paper we consider the second order nonlinear neutral delay Partial Difference Equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above Partial Difference Equation. Three nontrivial examples are given to illustrate the advantages of our results.
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Existence of Bounded Positive Solutions for Partial Difference Equations with Delays
Abstract and Applied Analysis, 2012Co-Authors: Z Liu, Young Chel Kwun, Shin Min KangAbstract:This paper deals with solvability of the third-order nonlinear Partial Difference Equation with delays . With the help of the Banach fixed-point theorem, the existence results of uncountably many bounded positive solutions for the Partial Difference Equation are given; some Mann iterative schemes with errors are suggested, and the error estimates between the iterative schemes and the bounded positive solutions are discussed. Three nontrivial examples illustrating the results presented in this paper are also provided.
B. G. Zhang - One of the best experts on this subject based on the ideXlab platform.
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Oscillation criteria of a class of Partial Difference Equations with delays
Computers & Mathematics With Applications, 2004Co-Authors: B. G. Zhang, C.j. TianAbstract:This paper is concerned with the linear delay Partial Difference Equation aA"m"+"1","n"+"1 + bA"m"+"1","n + cA"n"m","n"+"l - dA"m","n +p"m","nA "m"-"@s","n"-"@t = 0, where @s and @t are two nonnegative integers, a, b, c, and d are positive constants, and {p"i","j i, j @e N"0 is a double real sequence. Sufficient conditions for this Equation to be oscillatory are derived.
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Oscillation criteria of a class of Partial Difference Equations with delays
Computers & Mathematics with Applications, 2004Co-Authors: B. G. Zhang, C.j. TianAbstract:AbstractThis paper is concerned with the linear delay Partial Difference Equation aAm+1,n+1 + bAm+1,n + cAnm,n+l − dAm,n +pm,nA m−σ,n−τ = 0, where σ and τ are two nonnegative integers, a, b, c, and d are positive constants, and {pi,j i, j ε N0 is a double real sequence. Sufficient conditions for this Equation to be oscillatory are derived
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Comparison and linearized oscillation theorems for a nonlinear Partial Difference Equation
The ANZIAM Journal, 2001Co-Authors: B. G. ZhangAbstract:AbstractConnections between a linear Partial Difference Equation with constant coefficients and a nonlinear Partial Difference Equation are established by means of a comparison theorem and a continuous dependence of parameters theorem. A linearized oscillation theorem is also established as an application.
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Oscillation criteria of certain nonlinear Partial Difference Equations
Computers & Mathematics with Applications, 1999Co-Authors: B. G. Zhang, B.m. LiuAbstract:This paper is concerned with the nonlinear Partial Difference Equation with continuous variables A(x + a, y) + A(x, y +a) − A(x, y) + ∑i=1mhi(x, y, A(x − σi, y − τi)) = 0 , where a, σi, τi are positive numbers, hi(x, y, u) ϵ C(R+ × R+ × R, R), uhi(x, y, u) > 0 for u ≠ 0, hi is nondecreasing in u, i = 1, …, m. Some oscillation criteria of this Equation are obtained.
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Necessary and Sufficient Conditions for Oscillations of Linear Delay Partial Difference Equations
Discrete Dynamics in Nature and Society, 1998Co-Authors: B. G. Zhang, Shutang LiuAbstract:This paper is concerned with the linear delay Partial Difference Equation Am,n=∑i=1upiAm−ki,n−li
Z Liu - One of the best experts on this subject based on the ideXlab platform.
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uncountably many bounded positive solutions for a second order nonlinear neutral delay Partial Difference Equation
Bulletin of The Iranian Mathematical Society, 2015Co-Authors: Z Liu, J S Ume, Shin Min KangAbstract:In this paper we consider the second order nonlinear neutral delay Partial Difference Equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above Partial Difference Equation. Three nontrivial examples are given to illustrate the advantages of our results.
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Existence of Bounded Positive Solutions for Partial Difference Equations with Delays
Abstract and Applied Analysis, 2012Co-Authors: Z Liu, Young Chel Kwun, Shin Min KangAbstract:This paper deals with solvability of the third-order nonlinear Partial Difference Equation with delays . With the help of the Banach fixed-point theorem, the existence results of uncountably many bounded positive solutions for the Partial Difference Equation are given; some Mann iterative schemes with errors are suggested, and the error estimates between the iterative schemes and the bounded positive solutions are discussed. Three nontrivial examples illustrating the results presented in this paper are also provided.