Inclusion Theorems for Non-linear Difference Equations with Applications

DOI10.1080/10236190310001625280zbMath1056.39003OpenAlexW2044876987MaRDI QIDQ4469975

Lothar Berg

Publication date: 22 June 2004

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236190310001625280

zbMATH Keywords

boundary value problemsasymptotic behaviourinclusion theoremsnonlinear difference equationscomplete asymptotic expansionRiccati-like equations

Mathematics Subject Classification ID

Related Items (58)

Global stability and asymptotics of some classes of rational difference equations ⋮ Asymptotic behavior of the positive solutions of an exponential type system of difference equations ⋮ On the asymptotics of some difference equations ⋮ Existence of solutions with a single semicycle for a general second-order rational difference equation ⋮ Approximation and optimization of Darboux type differential inclusions with set-valued boundary conditions ⋮ On the positive nonoscillatory solutions of the difference equation \(x_{n+1}=\alpha+\Big(\dfrac{x_{n-k}}{x_{n-m}}\Big)^p\) ⋮ On a nonlinear second-order difference equation ⋮ The difference equation \(x_{n+1}=\alpha + \frac {x_{n-k}}{\Sigma_{i=0}^{k-1} c_{i}x_{n-i}}\) has solutions converging to zero ⋮ On a class of difference equations with interlacing indices ⋮ Global dynamics for a higher-order rational difference equation ⋮ Periodic solutions for a class of higher-order difference equations ⋮ Boundedness character of a fourth order nonlinear difference equation ⋮ On a class of higher-order difference equations ⋮ Existence, uniqueness and attractivity of prime period two solution for a difference equation of exponential form ⋮ On an exponential-type fuzzy difference equation ⋮ On integer parts of the reciprocal remainders of some sums ⋮ On the system of two difference equations of exponential form: \(x_{n+1}=a+bx_{n-1}e^{-y_n}\), \(y_{n+1}=c+dy_{n-1}e^{-x_n}\). ⋮ Asymptotic expansions for the sequences of the modified discrete delay logistic model type ⋮ Asymptotic expansions for the recurrence xn+1=1n∑k=1nfxkk$$ {x}_{n+1}=\frac{1}{n}\sum \limits_{k=1}^nf\left(\frac{x_k}{k}\right) $$ ⋮ Study of the asymptotic behavior of the solutions of three systems of difference equations of exponential form ⋮ Nontrivial solutions of a higher-order rational difference equation ⋮ A final result on the oscillation of solutions of the linear discrete delayed equation \({\Delta}x(n) = -p(n)x(n - k)\) with a positive coefficient ⋮ Unbounded solutions of the difference equation \(x_{n} = x_{n-l}x_{n-k} - 1\) ⋮ Global behavior of the difference equation \(x_{n+1}=(p+x_{n-1})/(qx_n+x_{n-1})\) ⋮ On a higher-order nonlinear difference equation ⋮ On global attractivity of a class of nonautonomous difference equations ⋮ Global behavior of two families of nonlinear symmetric difference equations ⋮ Existence of solutions for a coupled system of difference equations with causal operators ⋮ Existence of nontrivial solutions of a rational difference equation ⋮ Bounded solutions of a class of difference equations in Banach spaces producing controlled chaos ⋮ On a discrete epidemic model ⋮ On the recursive sequence \(x_{n+1}=A+x_{n}^{p}/x_{n-1}^{p}\) ⋮ Permanence for a generalized discrete neural network system ⋮ On the behaviour of the solutions of a second-order difference equation ⋮ Asymptotics of some classes of higher-order difference equations ⋮ A global convergence result for a higher order difference equation ⋮ Asymptotic periodicity of a higher-order difference equation ⋮ Dynamics of a class of higher order difference equations ⋮ On the difference equation \(x_{n+1}=x_nx_{n-2}-1\) ⋮ Corrigendum: Corrections to ‘Inclusion theorems for non-linear difference equations with applications’ ⋮ Asymptotic dynamics of a difference equation with a parabolic equilibrium ⋮ On positive solutions of a (\(k+1\))th order difference equation ⋮ On monotone solutions of some classes of difference equations ⋮ The global attractivity of the rational difference equation 𝑦_{𝑛}=𝐴+(\frac{𝑦_{𝑛-𝑘}}𝑦_{𝑛-𝑚})^{𝑝} ⋮ Boundedness character of positive solutions of a higher order difference equation ⋮ On the recursive sequence \(x_{n+1}=\frac{a x^p_{n-2m+1}}{b+cx_{n-2k}^{p-1}}\) ⋮ Eventually constant solutions of a rational difference equation ⋮ On the difference equation \(X_{n+1} = \alpha + \frac{x_{n-1}}{x_n}\) ⋮ Existence of monotone solutions of a difference equation ⋮ Qualitative behavior of difference equation of order two and positive nonoscillatory solutions ⋮ On the asymptotics of some systems of difference equations ⋮ A note on positive non-oscillatory solutions of the difference equation ⋮ On the dynamics of the solutions of a biological model ⋮ On a system of difference equations including negative exponential terms ⋮ A note for ``On the rational recursive sequence \(x_{n+1}=\frac{A+\sum^k_{i=0} \alpha_i x_{n-i}}{\sum^k_{i=0} \beta_ix_{n-i}}\) ⋮ On a class of third-order nonlinear difference equations ⋮ Dynamics for nonlinear difference equation \(x_{n+1}=(\alpha x_{n - k})/(\beta +\gamma x_{n - l}^p)\) ⋮ The behaviour of the positive solutions of the difference equation

Cites Work

• On the asymptotics of nonlinear difference equations
• Existence and approximation of solutions for first-order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutions

This page was built for publication: Inclusion Theorems for Non-linear Difference Equations with Applications