• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.245-256
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• 2005

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

• 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.16 no.1_2
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• pp.37-51
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• 2004

In this paper, we consider the asymptotic behavior of solutions of the forced nonlinear neutral difference equation $\Delta[x(n)-\sumpi(n)x(n-k_i)]+\sumqj(n)f(x(n-\iota_j))=r(n)$ with sign changing coefficients. Some sufficient conditions for every solution of (*) to tend to zero are established. The results extend and improve some known theorems in literature.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.79-90
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• 2004

In this paper the authors present sufficient conditions for all bounded solutions of the second order neutral difference equation ${\Delta}^2(y_n\;-\;py_{n-{\kappa}})\;-\;q_nf(y_{n-e})\;=\;0,\;n\;{\in}\;N$ to be oscillatory. Examples are provided to illustrate the results.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.31-37
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• 2003

In this Paper, we investigate local stability, oscillation and bounde-ness character of positive solutions of the difference equation $X_{N+l}$ = $\alpha$ + ( $X_{N-1}$$^{P/)}$( $X_{N}$$^{P}$), n = 0, 1, … under specified conditions.s.tions.s.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.87-99
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• 2002

We consider the problem of oscillation and nonoscillation solutions for unstable type second-order neutral difference equation : $\Delta^2(x(n))-p(n)x(n-\tau))=q(n)x(g(n))$. (1) In this paper, we obtain some conditions for the bounded solutions of Eq(1) to be oscillatory and for the existence of the nonoscillatory solutions.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.419-430
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• 2016

In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.