Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem by Weidong Lv

“…By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. …”
Get full text

Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional q-Difference Equation by Huiqin Chen, Shugui Kang, Lili Kong, Ying Gao

“…A class of boundary value problems of Caputo fractional q-difference equation is introduced. Green’s function and its properties for this problem are deduced. …”
Get full text

The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions by Chuanzhi Bai, Dandan Yang

“…In this work, we investigate the following system of fractional q-difference equations with four-point boundary problems: Dqαut+ft,vt=0,0<t<1;Dqβvt+gt,ut=0,0<t<1;u0=0,u1=γ1uη1; and v0=0,v1=γ2uη2, where Dqα and Dqβ are the fractional Riemann–Liouville q-derivative of order α and β, respectively, 0<q<1, 1<β≤α≤2, 0<η1,η2<1, 0<γ1η1α−1<1, and 0<γ2η2β−1<1. …”
Get full text

A Family of Integrable Differential-Difference Equations: Tri-Hamiltonian Structure and Lie Algebra of Vector Fields by Ning Zhang, Xi-Xiang Xu

“…Starting from a novel discrete spectral problem, a family of integrable differential-difference equations is derived through discrete zero curvature equation. …”
Get full text

Solvability of a Class of Generalized Neumann Boundary Value Problems for Second-Order Nonlinear Difference Equations by Jianye Xia, Yuji Liu

“…New sufficient conditions for the existence of at least one solution of the generalized Neumann boundary value problems for second order nonlinear difference equations ∇Δx(k)=f(k,x(k),x(k+1)), k∈[1,n−1], x(0)=ax(1), x(n)=bx(n−1), are established.…”
Get full text

On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) by Taixiang Sun, Hongjian Xi

“…We consider the following nonlinear difference equation: xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} and k,t∈{1,2,…} with 0≤m<t(k+1)−1, the initial values x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞), and {pn}n=0∞ is a positive sequence of the period k+1. …”
Get full text

Monotone Iterative Schemes for Positive Solutions of a Fractional q-Difference Equation with Integral Boundary Conditions on the Half-Line by Min Jiang, Rengang Huang

“…In this paper, we study the boundary value problem of a fractional q-difference equation with nonlocal integral boundary conditions on the half-line. …”
Get full text

Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero by R. N. Rath, J. G. Dix, B. L. S. Barik, B. Dihudi

“…We find necessary conditions for every solution of the neutral delay difference equation Δ(rnΔ(yn−pnyn−m))+qnG(yn−k)=fn to oscillate or to tend to zero as n→∞, where Δ is the forward difference operator Δxn=xn+1−xn, and pn, qn, rn are sequences of real numbers with qn≥0, rn>0. …”
Get full text

A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations by Fueyo, Sébastien, Chitour, Yacine

“…This paper proves a corona theorem for the algebra of Radon measures compactly supported in $\mathbb{R}_-$ and this result is applied to provide a necessary and sufficient Hautus–type frequency criterion for the $L^1$ exact controllability of linear controlled delayed difference equations (LCDDE). Hereby, it solves an open question raised in [5].…”
Get full text

Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian by Xiaofei He

“…By establishing a new proper variational framework and using the critical point theory, we establish some new existence criteria to guarantee that the 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian Δn(r(t−n)φp(Δnu(t−1)))+q(t)φp(u(t))=f(t,u(t+n),…,u(t),…,u(t−n)), n∈ℤ(3), t∈ℤ, has infinitely many homoclinic orbits, where φp(s) is p-Laplacian operator; φp(s)=|s|p−2s(1<p<∞)r, q, f are nonperiodic in t. …”
Get full text

Three-Point Boundary Value Problems of Nonlinear Second-Order q-Difference Equations Involving Different Numbers of q by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

“…We study a new class of three-point boundary value problems of nonlinear second-order q-difference equations. Our problems contain different numbers of q in derivatives and integrals. …”
Get full text

Chaotic numerical instabilities arising in the transition from differential to difference nonlinear equations by Alicia Serfaty de Markus

Subjects: Get full text

Delayed population models with Allee effects and exploitation by Eduardo Liz, Alfonso Ruiz-Herrera

Subjects: Get full text

Nondecreasing bounded continuous solutions of a <mml:math display="inline"><mml:mi>q</mml:mi></mml:math>-difference equation by Hou Yu Zhao, Shan Shan Guo

Get full text

On a class of third order neutral delay differential equations with piecewise constant argument by Garyfalos Papaschinopoulos

Subjects: Get full text

On the system of two nonlinear difference equations xn+1=A+xn−1/yn,   yn+1=A+yn−1/xn by G. Papaschinopoulos, C. J. Schinas

Subjects: “…System of two nonlinear difference equations…”
Get full text

Detection of the onset of numerical chaotic instabilities by lyapunov exponents by Alicia Serfaty De Markus

Subjects: “…Numerical instabilities; Difference equations; Lyapunov exponents; Fixed-step schemes; Chaos.…”
Get full text

On the Solutions of the System of Difference Equations xn+1=max{A/xn,yn/xn}, yn+1=max{A/yn,xn/yn} by Dağistan Simsek, Bilal Demir, Cengiz Cinar

“…We study the behavior of the solutions of the following system of difference equations xn+1=max⁡{A/xn,yn/xn}, yn+1=max⁡{A/yn,xn/yn} where the constant A and the initial conditions are positive real numbers.…”
Get full text

Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization by Krzysztof Fujarewicz, Krzysztof Łakomiec

Subjects: Get full text

Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 by Keying Liu, Peng Li, Weizhou Zhong

“…Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. …”
Get full text