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

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.569-578
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• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.127-144
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• 2005

In this paper, we consider the higher order nonlinear neutral delay difference equation of the form $\Delta^{\gamma}(x_{n}+px_{n-\gamma})+f(n, x_{n-\sigma_1(n)}, x_{n-\sigma_2(n)}, \ldots, x_{n-\sigma{_m}(n)})=0$. We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.439-448
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• 2023

We introduce several higher-order (p, q)-differential equation of which are related to (p, q)-Bernoulli polynomials. We also find some relations between (p, q)-Bernoulli, (p, q)-Euler, and (p, q)-Genocchi polynomials.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.29-40
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• 2009

Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.1-12
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• 2020

In this paper, we solve the difference equation $x_{n+1}={\frac{x_nx_{n-2}}{ax_n-bx_{n-2}}}$, n = 0, 1, …, where a and b are positive real numbers and the initial values x_-2, x_-1 and x₀ are real numbers. We also find invariant sets and discuss the global behavior of the solutions of aforementioned equation.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.439-445
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• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.507-516
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• 2016

In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation $$x_{n+1}={\frac{ax_{n-3}}{b-cx_{n-1}x_{n-3}}}$$, $n=0,1,{\ldots}$ where a, b, c are positive real numbers and the initial conditions $x_{-3}$, $x_{-2}$, $x_{-1}$, $x_0$ are real numbers.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.205-215
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• 2009

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.369-382
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• 2016

In this paper, we investigate the global behavior of the solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-2k-1}}{C+D\prod_{i=l}^{k}x_{n-2i}^{m_i}}$, n=0, 1, ..., with non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and m_i, i=l, k are positive integers.