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Oscillation properties for a scalar linear difference equation of mixed type

Leonid Berezansky;  Sandra Pinelas — 2016

Mathematica Bohemica

The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type Δ x ( n ) + ∑ k = - p q a k ( n ) x ( n + k ) = 0 , n > n 0 , where Δ x ( n ) = x ( n + 1 ) - x ( n ) is the difference operator and { a k ( n ) } are sequences of real numbers for k = - p , ... , q , and p > 0 , q ≥ 0 . We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.

Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments

Srinivasan Selvarangam;  Sethurajan A. Rupadevi;  Ethiraju Thandapani;  Sandra Pinelas — 2021

Mathematica Bohemica

In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation Δ 3 ( x n + a n x n - l + b n x n + m ) + p n x n - k - q n x n + r = 0 , n ≥ n 0 via Banach contraction principle. Examples are provided to illustrate the main results. The results obtained in this paper extend and complement some of the existing results.

Oscillation theorems for third order nonlinear delay difference equations

Kumar S. Vidhyaa;  Chinnappa Dharuman;  Ethiraju Thandapani;  Sandra Pinelas — 2019

Mathematica Bohemica

Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form Δ ( a n ( Δ ( b n ( Δ y n ) α ) ) ) + q n f ( y σ ( n ) ) = 0 to have property ( A ) or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.

Laplace - Fibonacci transform by the solution of second order generalized difference equation

Sandra Pinelas;  G. B. A. Xavier;  S. U. Vasantha Kumar;  M. Meganathan — 2017

Nonautonomous Dynamical Systems

The main objective of this paper is finding new types of discrete transforms with tuning factor t. This is not only analogy to the continuous Laplace transform but gives discrete Laplace-Fibonacci transform (LFt). This type of Laplace-Fibonacci transform is not available in the continuous case. The LFt generates uncountably many outcomes when the parameter t varies on (0,∞). This possibility is not available in the existing Laplace transform. All the formulae and results derived are verified by...

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