Browsing by Subject "nonoscillatory solution"

Now showing 1 - 6 of 6

Access status: Open Access ,
Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations
(2006) Migda, Małgorzata
In this paper we study asymptotic behavior of solutions of a higher order neutral difference equation of the form $\Delta^m(x_n+p_nx_{n-\tau})+f(n,x_{\sigma (n)})=h_n.$ We present conditions under which all nonoscillatory solutions of the above equation have the property $x_n = cn^{m-1}+o(n^{m-1})$ for some $c\in R$.
Access status: Open Access ,
Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations
(Wydawnictwa AGH, 2023) Naito, Manabu
We consider the half-linear differential equation $(|x'|^{\alpha}\mathrm{sgn}\,x')' + q(t)|x|^{\alpha}\mathrm{sgn}\,x = 0, \quad t \geq t_{0},$ under the condition $\lim_{t\to\infty}t^{\alpha}\int_{t}^{\infty}q(s)ds = \frac{\alpha^{\alpha}}{(\alpha+1)^{\alpha+1}}.$ It is shown that if certain additional conditions are satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as $t \to \infty$.
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 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.
Access status: Open Access ,
Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
(Wydawnictwa AGH, 2021) Naitō, Manabu
We consider the half-linear differential equation of the form $(p(t)|x'|^{\alpha}\mathrm{sgn} x')' + q(t)|x|^{\alpha}\mathrm{sgn} x = 0, \quad t\geq t_{0},$ under the assumption $\int_{t_{0}}^{\infty}p(s)^{-1/\alpha}ds =\infty$. It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as $t \to \infty$.