Browsing by Subject "neutral differential equations"

Now showing 1 - 3 of 3

Access status: Open Access ,
Novel oscillation criteria for third-order semi-canonical differential equations with an advanced neutral term
(Wydawnictwa AGH, 2025) Vidhyaa, Kumar S.; Thandapani, Ethiraju; Tunç, Ercan
The main purpose of this paper is to present new oscillation results for nonlinear semi-canonical third-order differential equations with an advanced neutral term. The main idea is first by reducing the studied semi-canonical equation into standard canonical type equation without assuming any extra conditions. Then, by using the comparison method and integral averaging technique, sufficient conditions are established to ensure the oscillation of the reduced canonical equation, which in turn leads to the oscillation of the original equation. Therefore, the technique used here is very useful since the results already known for the canonical equations can be applied to obtain the oscillation of the semi-canonical equations. Two examples are provided to illustrate the importance of the main results
Access status: Open Access ,
Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments
(2012) Elabbasy, Elmetwally M.; Hassan Abdelmonem, Taher Saleh; Moaaz, O.
Oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form $r(t)\psi(x(t))|z'(t)|^{\alpha -1} z'(t)+ \int_a^b q(t,\xi)f(x(g(t,\phi)))d\sigma (\xi) =0,\quad t\gt t_0,$ where $\alpha \gt 0$ and $z(t)= x(t)+p(t)x(t-\tau)$. Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results
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.