scholarly journals A HIGH ORDER DIFFERENCE METHOD FOR FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE SPATIALLY VARIABLE COEFFICIENTS UNDER PERIODIC BOUNDARY CONDITIONS

2020 ◽  
Vol 10 (2) ◽  
pp. 474-485
Author(s):  
Huiqin Zhang ◽  
◽  
Yan Mo ◽  
Zhibo Wang
Keyword(s):  
Boundary Conditions ◽  
Difference Method ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Variable Coefficients ◽  
High Order ◽  
Diffusion Equations ◽  
Order Difference

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.

scholarly journals Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications

2021 ◽  
Vol 41 (4) ◽  
pp. 489-507
Author(s):  
Abdelrachid El Amrouss ◽  
Omar Hammouti
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Critical Point Theory ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Difference Operator ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Existence Of A Solution ◽  
Order Difference

Let \(n\in\mathbb{N}^{*}\), and \(N\geq n\) be an integer. We study the spectrum of discrete linear \(2n\)-th order eigenvalue problems \[\begin{cases}\sum_{k=0}^{n}(-1)^{k}\Delta^{2k}u(t-k) = \lambda u(t) ,\quad & t\in[1, N]_{\mathbb{Z}}, \\ \Delta^{i}u(-(n-1))=\Delta^{i}u(N-(n-1)),\quad & i\in[0, 2n-1]_{\mathbb{Z}},\end{cases}\] where \(\lambda\) is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear \(2n\)-th order problems by applying the variational methods and critical point theory.

scholarly journals Positive Periodic Solutions for First-Order Difference Equations with Impulses

2021 ◽  
Author(s):  
Mesliza Mohamed ◽  
Gafurjan Ibragimov ◽  
Seripah Awang Kechil
Keyword(s):  
Boundary Conditions ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Positive Periodic Solutions ◽  
Order Difference ◽  
First Order

This paper investigates the first-order impulsive difference equations with periodic boundary conditions

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