• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.851-864
• /
• 2017

The problems of global and local exponential stability analysis of a class of nonlinear non-autonomous difference equations in Banach spaces are studied in this paper. By a novel comparison technique, new explicit exponential stability conditions are derived. Numerical examples are given to illustrate the effectiveness of the obtained results.

• The Pure and Applied Mathematics
• /
• v.24 no.4
• /
• pp.191-200
• /
• 2017

The theory of $u_0-positive$ operators is applied to obtain smallest eigenvalue comparison results for right focal boundary value problems of Atici-Eloe fractional difference equations.

• Journal of applied mathematics & informatics
• /
• v.41 no.1
• /
• pp.167-179
• /
• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.409-431
• /
• 2022

In this paper, we deal with the existence of solutions of the following system of nonlinear rational difference equations with order five $x_{n+1}=\frac{y_{n-3}x_{n-4}}{y_n(a+by_{n-3}x_{n-4})}$, $y_{n+1}=\frac{x_{n-3}y_{n-4}}{x_n(c+dx_{n-3}y_{n-4})}$, n = 0, 1, ⋯, where parameters a, b, c and d are not executed at the same time and initial conditions x_-4, x_-3, x_-2, x_-1, x₀, y_-4, y_-3, y_-2, y_-1 and y₀ are non zero real numbers.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.299-312
• /
• 2008

In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

• Kyungpook Mathematical Journal
• /
• v.47 no.3
• /
• pp.425-438
• /
• 2007

In this paper, we establish some new oscillation criteria for a second-order delay dynamic equation $$u^{{\Delta}{\Delta}}(t)+p(t)u(\tau(t))=0$$ on a time scale $\mathbb{T}$. The results can be applied on differential equations when $\mathbb{T}=\mathbb{R}$, delay difference equations when $\mathbb{T}=\mathbb{N}$ and for delay $q$-difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for q > 1.

• Communications of the Korean Mathematical Society
• /
• v.24 no.4
• /
• pp.617-628
• /
• 2009

We present an efficient and accurate finite-difference method for computing Black-Scholes partial differential equations with multiunderlying assets. We directly solve Black-Scholes equations without transformations of variables. We provide computational results showing the performance of the method for two underlying asset option pricing problems.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.59-66
• /
• 2003

The object of the present paper is to establish some criteria of the convergence of all bounded solutions of (1), (1').

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.489-501
• /
• 2003

In this paper we shall consider the nonlinear delay difference equation $\Delta({p_n}{\Deltax_N})\;+\;q_nf(x_{n-\sigma})\;=\;0,\;n\;=\;0,\;1,\;2,\;...$ when (equation omitted). We will establish some sufficient conditions which guarantee that every solution is oscillatory or converges to zero.

• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.785-795
• /
• 2018

In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.