scholarly journals Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhinan Xia
Keyword(s):  
Fixed Point ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Exponential Dichotomy ◽  
Second Order ◽  
Order Difference ◽  
Asymptotically Periodic ◽  
Asymptotic Periodicity ◽  
Asymptotically Periodic Solution ◽  
Composition Theorem

We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.

scholarly journals On the Second-Order Quantum (p,q)-Difference Equations with Separated Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chanon Promsakon ◽  
Nattapong Kamsrisuk ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Separated Boundary Conditions

In this paper, we investigate the existence and uniqueness of solutions for a boundary value problem for second-order quantum (p,q)-difference equations with separated boundary conditions, by using classical fixed point theorems. Examples illustrating the main results are also presented.

scholarly journals Positive Solutions for a System of Neumann Boundary Value Problems of Second-Order Difference Equations Involving Sign-Changing Nonlinearities

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jiqiang Jiang ◽  
Johnny Henderson ◽  
Jiafa Xu ◽  
Zhengqing Fu
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Difference Equations ◽  
Fixed Point Index ◽  
Neumann Boundary ◽  
Second Order ◽  
Point Index ◽  
Order Difference ◽  
Existence Of Positive Solutions ◽  
Neumann Boundary Value Problems

In this paper, we study the existence of positive solutions for the system of second-order difference equations involving Neumann boundary conditions: -Δ2u1(t-1)=f1(t,u1(t),u2(t)), t∈[1,T]Z, -Δ2u2(t-1)=f2(t,u1(t),u2(t)), t∈[1,T]Z, Δui(0)=Δui(T)=0, i=1,2, where T>1 is a given positive integer, Δu(t)=u(t+1)-u(t), and Δ2u(t)=Δ(Δu(t)). Under some appropriate conditions for our sign-changing nonlinearities, we use the fixed point index to establish our main results.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

scholarly journals On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 476
Author(s):  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

Spectrum theory of second-order difference equations with indefinite weight

2018 ◽  
Vol 8 (3) ◽  
pp. 971-985
Author(s):  
Ruyun Ma ◽  
Chenghua Gao ◽  
Yanqiong Lu
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Indefinite Weight ◽  
Order Difference
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