Results 11 to 20 of about 214,223 (194)
Oscillation theorems for third order nonlinear delay difference equations [PDF]
Mathematica Bohemica, 2019 Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form \Delta(a_n(\Delta(b_n(\Delta y_n)^{\alpha})))+q_nf(y_{\sigma(n)})=0 to have property ${(\rm A)}$ or to be oscillatory.
Kumar S. Vidhyaa +3 more
doaj +4 more sources
Linear Third-Order Difference Equations: Oscillatory and Asymptotic Behavior [PDF]
Rocky Mountain Journal of Mathematics, 1992 A point of contact of the graph of \(U = \{U_ n\}\) satisfying (1) \(\Delta^ 3U_ n + P_{n+1}\Delta U_{n+2} + Q_ nU_{n+2} = 0\), with the real axis is a node. A solution of (1) is said to be oscillatory if it has arbitrarily large nodes. It is proved that (1) always has an oscillatory solution.
B. Smith
openalex +4 more sources
Oscillation of nonlinear third order perturbed functional difference equations [PDF]
Nonautonomous Dynamical Systems, 2019 This paper deals with oscillatory and asymptotic behavior of all solutions of perturbed nonlinear third order functional difference ...
Dinakar P. +2 more
doaj +2 more sources
Oscillation of third-order nonlinear delay difference equations
Turkish Journal of Mathematics, 2012 Third-order nonlinear difference equations of the form Δ(cnΔ(dnΔxn)) + pnΔxn+1 + qnf (xn−σ )= 0 ,n ≥ n0 are considered. Here, {cn} , {dn} , {pn} ,a nd{qn} are sequences of positive real numbers for n0 ∈ N, f is a continuous function such that f (u) /u ≥ K> 0f oru 0 .
Mustafa Fahri Aktaş +2 more
openalex +4 more sources
Oscillation and nonoscillation in nonlinear third order difference equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 1989 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B. Smith, W. E. Taylor
openalex +4 more sources
Stability of the third order rational difference equation
MANAS: Journal of Engineering, 2020 In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\]where the initial conditions are non zero real numbers and are ...
Mehmet Emre Erdoğan
doaj +2 more sources
On a Third‐Order System of Difference Equations with Variable Coefficients [PDF]
Abstract and Applied Analysis, 2012 We show that the system of three difference equations , , and , n ∈ ℕ0, where all elements of the sequences , , , n ∈ ℕ0, i ∈ {1,2, 3}, and initial values x−j, y−j, z−j, j ∈ {0,1, 2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when ...
Stevo Stević +3 more
openalex +6 more sources
Boundary-value problems for nonlinear third-order q-difference equations
Electronic Journal of Differential Equations, 2011 Summary: This article shows existence results for a boundary-value problem of nonlinear third-order \(q\)-difference equations. Our results are based on Leray-Schauder degree theory and some standard fixed point theorems.
Bashir Ahmad
openalex +3 more sources
Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments [PDF]
Mathematica Bohemica, 2021 In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation \Delta^3(x_n+a_n x_{n-l} +b_n x_{n+m})+p_n x_{n-k} - q_n x_{n+r}=0,\quad n\geq n_0 ...
Srinivasan Selvarangam +3 more
doaj +1 more source
Explicit bounds for third-order difference equations [PDF]
The ANZIAM Journal, 2006 AbstractThis paper gives explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher-order equations. The results extend recent work of the authors for second-order equations.
Berenhaut, Kenneth S. +2 more
openaire +1 more source