Results 1 to 10 of about 214,223 (194)

Analytical Solution to a Third-Order Rational Difference Equation [PDF]

The Scientific World Journal, 2023
Inspired by some open conjectures in a rational dynamical system by G. Ladas and Palladino, in this paper, we consider the problem of solving a third-order difference equation. We comment the conjecture by Ladas.
Alvaro H. Salas S., Gilder Cieza Altamirano, Rafaél Artidoro Sandoval Núñez   +2 more
doaj   +4 more sources

On third-order linear difference equations involving quasi-differences [PDF]

Advances in Difference Equations, 2006
We study the third-order linear difference equation with quasi-differences and its adjoint equation. The main results of the paper describe relationships between the oscillatory and nonoscillatory solutions of both equations.
Došlá Zuzana, Kobza Aleš
doaj   +7 more sources

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.
R. Abo-Zeid, R Abo-Zeid, R Abo-Zeid, R Abo-Zeid, R Abo-Zeid, R Abo-Zeid, R Abo-Zeid, A Amleh, E Camouzis, G Ladas, A Amleh, E Camouzis, G Ladas, A Anisimova, I Bula, I Bajo, I Bajo, E Liz, I Bajo, D Franco, J Pern, F Balibrea, A Cascales, M Dehghan, C Kent, R Mazrooei-Sebdani, N Ortiz, H Sedaghat, E Jankowski, M Kulenovi, C Kent, H Sedaghat, V Kocic, G Ladas, M Kulenovi, G Ladas, H Sedaghat, H Shojaei, S Parvandeh, T Mohammadi, Z Mohammadi, N Mohammadi, I Szalkai   +42 more
openalex   +3 more sources

Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations [PDF]

Mathematica Bohemica, 2023
We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation D_3y(n)+f(n)y^\beta(\sigma(n))=0, where $D_3 y(n)=\Delta(b(n)\Delta(a(n)(\Delta y(n))^\alpha))$ is studied.
Govindasamy Ayyappan, George E. Chatzarakis, Thaniarasu Kumar, Ethiraj Thandapani   +3 more
doaj   +2 more sources

Third order non-linear difference equation with neutral term [PDF]

E3S Web of Conferences, 2023
This paper aims to investigate the oscillatory characteristics of a neutral third order nonlinear difference equation. Utilizing the comparison principle, we get some new standards that guarantee that any solution to the neutral difference equation ...
Kaleeswari S., Rangasri S.
doaj   +2 more sources

Asymptotic properties of solutions of third order difference equations

Applicable Analysis and Discrete Mathematics, 2020
We consider the difference equation of the form ?(rn?(pn?xn)) = anf (x?(n)) + bn. We present sufficient conditions under which, for a given solution y of the equation ?(rn?(pn?yn)) = 0, there exists a solution x of the nonlinear equation with the asymptotic behavior xn = yn + zn, where z is a sequence convergent to zero.
Janusz Migda, Małgorzata Migda, Magdalena Nockowska‐Rosiak   +2 more
openalex   +4 more sources

Quasi‐adjoint third order difference equations: oscillatory and asymptotic behavior [PDF]

International Journal of Mathematics and Mathematical Sciences, 1987
In this paper, asymptotic properties of solutions of urn:x-wiley:01611712:media:ijmm806976:ijmm806976-math-0001 are investigated via the quasi‐adjoint equation urn:x-wiley:01611712:media:ijmm806976:ijmm806976-math-0002 A necessary and sufficient condition for the existence of oscillatory solutions of (E+) is given.
B. Smith
openalex   +7 more sources

Oscillatory behavior of third order nonlinear difference equation with mixed neutral terms

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this paper, we obtain some new sufficient conditions for the oscillation of all solutions of the third order nonlinear neutral difference equation of the form \begin{equation*} \Delta^3 \left(x_n+b_n x_{n-\tau_{1}}+c_n x_{n+\tau_{2}}\right)^{\alpha} =
Ethiraju Thandapani, S. Selvarangam, Seghar Devarajalu   +2 more
doaj   +2 more sources

On the oscillation of third order half-linear neutral type difference equations

Electronic Journal of Qualitative Theory of Differential Equations, 2011
In this paper, the authors study the oscillatory properties of third order quasilinear neutral difference equation of the form $$\Delta(a_{n}(\Delta^{2}(x_{n} + p_{n}x_{n-\delta}))^{\alpha}) + q_{n} {x^{\alpha}_{n-\tau}} = 0,\quad n\geq 0, \tag{E ...
Ethiraju Thandapani, M. Vijaya, Tongxing Li   +2 more
doaj   +2 more sources

Attractivity of two nonlinear third order difference equations

Journal of the Egyptian Mathematical Society, 2013
Consider the difference equations \[ x_{n+1}=\frac{A-Bx_{n-1}}{C+Dx_{n-2}},\;n=0,1,2,\dots,\tag{\(*\)} \] where \(A,B\) are nonnegative, \(D>0\) and \(C\) is a nonzero real number. Also, \(C+Dx_{n-2}\neq 0\) for all \(n\geq 0\). The author investigates the global attractivity, periodic nature, oscillation and boundedness of all admissible solutions of ...
R. Abo-Zeid
openalex   +2 more sources