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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Oscillatory And Asymptotic Behavior Of Third-Order Nonlinear Differential Equations With A Superlinear Neutral Term, Said R. Grace, Iren Jadlovska, Ercan Tunç
Turkish Journal of Mathematics
Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations with a superlinear neutral term to be either oscillatory or convergent to zero asymptotically. Examples illustrating the results are included and some suggestions for further research are indicated.
New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra
New Criteria For The Oscillation And Asymptotic Behavior Of Second-Order Neutral Differential Equations With Several Delays, Başak Karpuz, Shyam Sundar Santra
Turkish Journal of Mathematics
In this paper, necessary and sufficient conditions for asymptotic behavior are established of the solutions to second-order neutral delay differential equations of the form \begin{equation} \frac{d}{d{}t}\Biggl(r(t)\biggl(\frac{d}{d{}t}[x(t)-p(t)x(\tau(t))]\biggr)^{\gamma}\Biggr)+\sum_{i=1}^{m}q_{i}(t)f_{i}\bigl(x(\sigma_{i}(t))\bigr)=0 \quad\text{for}\ t\geq{}t_{0}.\nonumber \end{equation} We consider two cases when $f_{i}(u)/u^{\beta}$ is nonincreasing for $\gamma>\beta$, and nondecreasing for $\beta>\gamma$, where $\beta$ and $\gamma$ are quotients of two positive odd integers. Our main tool is Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.
A Reduced Computational Matrix Approach With Convergence Estimation For Solving Model Differential Equations Involving Specific Nonlinearities Of Quartic Type, Ömür Kivanç Kürkçü
A Reduced Computational Matrix Approach With Convergence Estimation For Solving Model Differential Equations Involving Specific Nonlinearities Of Quartic Type, Ömür Kivanç Kürkçü
Turkish Journal of Mathematics
This study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-$\alpha$, matrix equations, and Chebyshev--Lobatto collocation points. The simplicity of the method provides fast computation while eliminating an algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes the consistency of the solutions due to the parameter-$\alpha$. The oscillatory behavior of the obtained solutions on long time intervals is simulated via a coupled …
Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat
Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat
Turkish Journal of Mathematics
In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form% \begin{equation} \Delta (r_{n}(\Delta ^{k-1}(y_{n}+p_{n}y_{\tau _{n}}))+q_{n}f(y_{\sigma _{n}})=0\text{, }n\geq n_{0}\text{,} \tag{0.1} \end{equation}% where $r_{n},p_{n},q_{n}\in \lbrack n_{0},\infty ),$ $r_{n}>0$, $q_{n}>0$; $% 0\leq p_{n}\leq p_{0}0$; $\tau _{\sigma }=\sigma _{\tau }$; $\frac{f(u)}{u}\geq m>0$ for $u\neq 0$. Moreover, we provide some examples to illustrate our main results.
On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov
On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov
Turkish Journal of Mathematics
We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation $\Delta y(n)=-g(n)y(n-k)$. We assume that the coefficient of this equation oscillates at the certain level and the oscillation amplitude decreases as $n\to\infty$. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotic formulae. The obtained results are applied to the oscillation and stability problems for the solutions of the considered equation.