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 NONEXISTENCE OF POSITIVE SOLUTIONS OF A NONLINEAR PARTIAL DIFFERENCE EQUATION

1997 ◽  
Vol 28 (1) ◽  
pp. 51-58
Author(s):  
SHU-TANG LIU ◽  
SUI-SUN CHENG
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Characteristic Equation ◽  
Difference Equations ◽  
Necessary Conditions ◽  
Partial Difference Equation ◽  
Partial Difference ◽  
Existence Of Positive Solutions ◽  
Positive Roots

Necessary conditions are derived for the existence of positive solutions of a class of nonlinear partiai' difference equations. The technique used to derive these conditions is based on the nonexistence of positive roots of an associated characteristic equation.

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 ON EXISTENCE OF POSITIVE SOLUTIONS OF NEUTRAL DIFFERENCE EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 257-265
Author(s):  
J. H. SHEN ◽  
Z. C. WANG ◽  
X. Z. QIAN
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Positive Solution ◽  
Positive Solutions ◽  
Difference Equations ◽  
Real Numbers ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Existence Of Positive Solutions

Consider the neutral difference equation \[\Delta(x_n- cx_{n-m})+p_nx_{n-k}=0, n\ge N\qquad (*) \] where $c$ and $p_n$ are real numbers, $k$ and $N$ are nonnegative integers, and $m$ is positive integer. We show that if \[\sum_{n=N}^\infty |p_n|<\infty \qquad (**) \] then Eq.(*) has a positive solution when $c \neq 1$. However, an interesting example is also given which shows that (**) does not imply that (*) has a positive solution when $c =1$.

scholarly journals Asymptotic Behavior of Solutions to Half-Linearq-Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Pavel Řehák
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Special Limit ◽  
Bounded Functions ◽  
Necessary And Sufficient

We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linearq-difference equationDq(Φ(Dqy(t)))+p(t)Φ(y(qt))=0,t∈{qk:k∈N0}withq>1,Φ(u)=|u|α−1sgn⁡uwithα>1, to behave likeq-regularly varying orq-rapidly varying orq-regularly bounded functions (that is, the functionsy, for which a special limit behavior ofy(qt)/y(t)ast→∞is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.

scholarly journals Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Zhijian Wei ◽  
Meitao Le
Keyword(s):  
Mathematical Models ◽  
Positive Solutions ◽  
Difference Equations ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Nonlinear Difference Equations ◽  
System Of Difference Equations ◽  
Discrete Epidemic Model ◽  
Existence Of Positive Solutions

We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results.

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