Necessary and sufficient conditions for the existence of positive solutions of nonlinear difference equations

2004 ◽  
pp. 385-396
Author(s):  
R. Zhang ◽  
Z. Wang ◽  
J. Yu
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Nonlinear Difference Equations ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

scholarly journals On the Periodicity of General Class of Difference Equations

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 75 ◽  
Author(s):  
Osama Moaaz ◽  
Hamida Mahjoub ◽  
Ali Muhib
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
General Class ◽  
Sufficient Conditions ◽  
Usual Method ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient

In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method.

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.

scholarly journals On the existence of positive solutions for periodic parabolic sublinear problems

2003 ◽  
Vol 2003 (17) ◽  
pp. 975-984 ◽  
Author(s):  
T. Godoy ◽  
U. Kaufmann
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Wide Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Parabolic Problems ◽  
Smooth Bounded Domain ◽  
Carathéodory Functions ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problemsLu=g(x,t,u)inΩ×ℝ(whereΩ⊂ℝNis a smooth bounded domain) for a wide class of Carathéodory functionsg:Ω×ℝ×[0,∞)→ℝsatisfying some integrability and positivity conditions.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

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