Browsing by Subject "third order"

Now showing 1 - 4 of 4

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 ,
Oscillation criteria for third order nonlinear delay differential equations with damping
(2015) Grace, Said R.
This note is concerned with the oscillation of third order nonlinear delay differential equations of the form $\left( r_{2}(t)\left( r_{1}(t)y^{\prime}(t)\right)^{\prime}\right)^{\prime}+p(t)y^{\prime}(t)+q(t)f(y(g(t)))=0.\tag{$\ast$}$ $(*)$ In the papers [A.Tiryaki, M.F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007), 54-68] and [M.F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear-functional differential equations, Applied Math. Letters 23 (2010), 756-762], the authors established some sufficient conditions which insure that any solution of equation $(*)$ oscillates or converges to zero, provided that the second order equation $\left( r_{2}(t)z^{\prime }(t)\right)^{\prime}+\left(p(t)/r_{1}(t)\right) z(t)=0\tag{$\ast\ast$}$ $(**)$ is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation $(*)$ oscillates if equation $(**)$ is nonoscillatory. We also establish results for the oscillation of equation $(*)$ when equation $(**)$ is oscillatory.
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.