Browsing by Subject "oscillatory solution"

Now showing 1 - 6 of 6

Access status: Open Access ,
Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
(2006) Mikołajski, Jarosław; Schmeidel, Ewa
Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.
Access status: Open Access ,
Improved iterative oscillation tests for first-order deviating differential equations
(Wydawnictwa AGH, 2018) Chatzarakis, George E.; Jadlovská, Irena
In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing $\lim \sup$ and $\lim \inf$ on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
Access status: Open Access ,
Oscillations of equations caused by several deviating arguments
(Wydawnictwa AGH, 2019) Chatzarakis, George E.
Linear delay or advanced differential equations with variable coefficients and several not necessarily monotone arguments are considered, and some new oscillation criteria are given. More precisely, sufficient conditions, involving $\lim\sup$ and $\lim\inf$, are obtained, which essentially improve several known criteria existing in the literature. Examples illustrating the results are also given, numerically solved in MATLAB.
Access status: Open Access ,
Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation
(Wydawnictwa AGH, 2017) Graef, John R.; Tunҫ, Ercan; Grace, Said R.
This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.
Access status: Open Access ,
Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
(2006) Schmeidel, Ewa
In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.
Access status: Open Access ,
Oscillatory properties of fourth order nonlinear difference equations with quasidifferences
(2006) Schmeidel, Ewa; Migda, Małgorzata; Musielak, Anna
In this paper we present the oscillation criterion for a class of fourth order nonlinear difference equations with quasidifferences.