Existence of positive solutions of systems of Volterra nonlinear difference equations

2006 ◽  
Vol 9 (1) ◽  
pp. 34-45 ◽  
Author(s):  
Jiang Zhu ◽  
Xiaolan Liu
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Existence Of Positive Solutions

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.

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 A family of nonlinear difference equations: Existence, uniqueness, and asymptotic behavior of positive solutions

2015 ◽  
Vol 193 ◽  
pp. 39-55 ◽  
Author(s):  
Saud M. Alsulami ◽  
Paul Nevai ◽  
József Szabados ◽  
Walter Van Assche
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Nonlinear Difference Equations
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