Results 31 to 40 of about 1,849,360 (286)

Periodic Solutions to a Third-Order Conditional Difference Equation over the Integers

Discrete Dynamics in Nature and Society, 2011
This paper studies a third-order conditional difference equation which is a generalization from the literature. We investigate this equation by transforming it into a first-order system. Finally it is proved that the equation has no period-two (or three)
Li He, Wanping Liu
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Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation [PDF]

, 2008
The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second
Alan K Common, Andrew N W Hone, Clarkson P A, Clarkson P A, Common A K, Common A K, Common A K, Cresswell C, Fukutani S, Hafev S T, Hamamoto T, Hone A N W, Ince E L, Isojima S, Jones W B, Joshi N, Kajiwara K, Kajiwara K, Kajiwara K, Kajiwara K, Nijhoff F, Ramani A, Satsuma J, Suris Y B, Taneda M, Vorob'ev A P, Yablonskii A I   +26 more
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On Positive Solutions and Mann Iterative Schemes of a Third Order Difference Equation

Abstract and Applied Analysis, 2014
The existence of uncountably many positive solutions and convergence of the Mann iterative schemes for a third order nonlinear neutral delay difference equation are proved. Six examples are given to illustrate the results presented in this paper.
Zeqing Liu, Heng Wu, Shin Min Kang, Young Chel Kwun   +3 more
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ON A THIRD ORDER DIFFERENCE EQUATION

Acta Universitatis Apulensis, 2018
Summary: In this paper, the authors solve the difference equation \[ x_{n+1} =\frac{x_nx_{n-2}}{-ax_n + bx_{n-2}}, \quad n = 0, 1, \dots, \] where \(a\) and \(b\) are positive real numbers and the initial values \(x_{-2}, x_{-1}\) and \(x_0\) are real numbers.
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Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation

, 1999
We consider the polynomials $\phi_n(z)= \kappa_n (z^n+ b_{n-1} z^{n-1}+ >...)$ orthonormal with respect to the weight $\exp(\sqrt{\lambda} (z+ 1/z)) dz/2 \pi i z$ on the unit circle in the complex plane.
Chie Bing Wang, Fokas A S, Hastings S P, Hisakado M, Jimbo M, Szegö G, Tracy C A, Tracy C A, Tracy C A, Tracy C A   +9 more
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Equivalent resistance of irregular 3 × n Hammock resistor network

Nantong Daxue xuebao. Ziran kexue ban, 2022
The equivalent resistance of a kind of irregular 3 × n Hammock resistor network is studied by the RT-I theory, in which the third order matrix equation and the third order boundary condition equation are established by Kirchhoff′s law and the branch ...
TAN Zhizhong
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Representation of solutions of a solvable nonlinear difference equation of second order

Electronic Journal of Qualitative Theory of Differential Equations, 2018
We present a representation of well-defined solutions to the following nonlinear second-order difference equation $$x_{n+1}=a+\frac{b}{x_n}+\frac{c}{x_nx_{n-1}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c$, and initial values $x_{-1}$ and $x_0 ...
Stevo Stevic, Bratislav Iricanin, Witold Kosmala, Zdenek Smarda   +3 more
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Positive solutions of a discrete nonlinear third-order three-point eigenvalue problem with sign-changing Green's function

Open Mathematics, 2021
In this paper, we discuss the existence of positive solutions to a discrete third-order three-point boundary value problem. Here, the weight function a(t)a\left(t) and the Green function G(t,s)G\left(t,s) both change their sign.
Cao Xueqin, Gao Chenghua, Duan Duihua
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OSCILLATORY PROPERTIES OF THIRD ORDER NEUTRAL DELAY DIFFERENCE EQUATIONS

Demonstratio Mathematica, 2002
This paper is devoted to the oscillatory properties of a third order neutral difference equation of the form \[ \Delta \left( c_n\Delta \left( d_n\Delta \left( y_n+p_ny_{n-k}\right) \right) \right) +q_nf\left( y_{n-m}\right) =e_n. \] Some sufficient conditions are obtained for oscillation of the solutions of the above equation.
Thandapani, E., Mahalingam, K.
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Semi-classical Laguerre polynomials and a third order discrete integrable equation

, 2009
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we use is
Christoffel E B, Darboux G, Forrester P J Witte N S, Forrester P J Witte N S, Frank W Nijhoff, Freud G, Grammaticos B, Laguerre E, Laguerre E, Laguerre E, Lax P D, Magnus A P, Paul E Spicer   +12 more
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