scholarly journals A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Syed Sabyel Haider ◽  
Mujeeb Ur Rehman ◽  
Thabet Abdeljawad
Keyword(s):  
Difference Equation ◽  
Discrete Time ◽  
Existence And Uniqueness ◽  
Transformation Method ◽  
Laplace Transforms ◽  
Partial Difference Equation ◽  
Transform Method ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Discrete Setting

The aim of this study is to develop a transform method for discrete calculus. We define the double Laplace transforms in a discrete setting and discuss its existence and uniqueness with some of its important properties. The delta double Laplace transforms have been presented for integer and noninteger order partial differences. For illustration, the delta double Laplace transforms are applied to solve partial difference equation.

scholarly journals Existence of positive solutions for certain partial difference equations

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Binggen Zhang ◽  
Qiuju Xing
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Partial Difference Equation ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Existence Of Positive Solutions

We give some sufficient conditions for the existence of positive solutions of partial difference equationaAm+1,n+1+bAm,n+1+cAm+1,n−dAm,n+Pm,nAm−k,n−1=0by two different methods.

scholarly journals Existence of Bounded Positive Solutions for Partial Difference Equations with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Zeqing Liu ◽  
Zhihua Wu ◽  
Young Chel Kwun ◽  
Shin Min Kang
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Partial Difference Equation ◽  
Third Order ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Iterative Schemes ◽  
The Third

This paper deals with solvability of the third-order nonlinear partial difference equation with delaysΔn(am,nΔm2(xm,n+bm,nxm-τ0,n-σ0))+f(m,n,xm-τ1,m,n-σ1,n,…,xm-τk,m,n-σk,n)=cm,n,  m≥m0,  n≥n0. 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.

scholarly journals Oscillation of certain partial difference equations

1998 ◽  
Vol 2 (4) ◽  
pp. 257-265 ◽  
Author(s):  
Sung Kyu Choi ◽  
Bing Gen Zhang
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Partial Difference Equation ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Oscillation Result ◽  
All Solutions ◽  
Sufficiency Conditions

We first obtain sufficiency conditions for the oscillation of all solutions of linear partial difference equationaAm+1,n+1+bAm+1,n+cAm,n+1−dAm,n+Pm,nAm−k,n−1=0. Next, we establish a linearized oscillation result for the nonlinear partial difference equationAm+1,n+1+Am+1,n+Am,n+1−Am,n+Pm,n f(Am−k,n−l)=0.

scholarly journals Partial difference equation method for lattice path problems

1999 ◽  
Vol 3 (2-4) ◽  
pp. 265-275 ◽  
Author(s):  
R. Brak ◽  
J. W. Essam ◽  
A. L. Owczarek
Keyword(s):  
Difference Equation ◽  
Lattice Path ◽  
Equation Method ◽  
Partial Difference Equation ◽  
Partial Difference
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