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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Turkish Journal of Mathematics
In this paper the second-order difference equations of the form \[ \Delta^2 x_n=a_nf(n,x_{\sigma(n)})+b_n \] are considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. In particular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study the asymptotic behavior of solutions.
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.
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
On Oscillatory And Nonoscillatory Behavior Of Solutions For A Class Of Fractional Orderdifferential Equations, Arjumand Seemab, Mujeeb Ur Rehman
Turkish Journal of Mathematics
This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t) _{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan
On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan
Turkish Journal of Mathematics
The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.
Solvability Of A System Of Nonlinear Difference Equations Of Higher Order, Merve Kara, Yasi̇n Yazlik
Solvability Of A System Of Nonlinear Difference Equations Of Higher Order, Merve Kara, Yasi̇n Yazlik
Turkish Journal of Mathematics
In this paper, we show that the following higher-order system of nonlinear difference equations, $ x_{n}=\frac{x_{n-k}y_{n-k-l}}{y_{n-l}\left( a_{n}+b_{n}x_{n-k}y_{n-k-l}\right)}, \ y_{n}=\frac{y_{n-k}x_{n-k-l}}{x_{n-l}\left( \alpha_{n}+\beta_{n}y_{n-k}x_{n-k-l}\right)}, \ n\in \mathbb{N}_{0}, $ where $k,l\in \mathbb{N}$, $\left(a_{n} \right)_{n\in \mathbb{N}_{0}}, \left(b_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\alpha_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\beta_{n} \right)_{n\in \mathbb{N}_{0}}$ and the initial values $x_{-i}, \ y_{-i}$, $i=\overline {1,k+l}$, are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case $k=2, l=k$.
Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz
Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz
Turkish Journal of Mathematics
In this paper we investigate the Volterra difference equation of the form $ \D(r_n\D x_n)=b_n+\sum_{k=1}^{n}K(n,k)f(x_k). $ We establish sufficient conditions for the existence of a solution $x$ of the above equation with the property $ x_n=y_n+\o(n^s), $ where $y$ is a given solution of the equation $\D(r_n\D y_n)=b_n$ and $s$ is nonpositive real number. We also obtain sufficient conditions for the existence of asymptotically periodic solutions.
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson
Turkish Journal of Mathematics
In this paper we study the Caputo and Riemann--Liouville nabla $(q,h)$-fractional difference equation and obtain the following two main results: Assume $0
On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
On A Solvable Nonlinear Difference Equation Of Higher Order, Durhasan Turgut Tollu, Yasi̇n Yazlik, Necati̇ Taşkara
Turkish Journal of Mathematics
In this paper we consider the following higher-order nonlinear difference equation $$ x_{n}=\alpha x_{n-k}+\frac{\delta x_{n-k}x_{n-\left( k+l\right) }}{\beta x_{n-\left( k+l\right) }+\gamma x_{n-l}},\ n\in \mathbb{N} _{0}, $$ where $k$ and $l$ are fixed natural numbers, and the parameters $\alpha $, $ \beta $, $\gamma $, $\delta $ and the initial values $x_{-i}$, $i=\overline{ 1,k+l}$, are real numbers such that $\beta ^{2}+\gamma ^{2}\neq 0$. We solve the above-mentioned equation in closed form and considerably extend some results in the literature. We also determine the asymptotic behavior of solutions and the forbidden set of the initial values using the obtained formulae for the case …
Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May
Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May
Turkish Journal of Mathematics
In this short note, we recover by a different method the new result due to Attouch, Chbani, Peyrouqet, and Redont concerning the weak convergence as $t\rightarrow+\infty$ of solutions $x(t)$ to the second-order differential equation $x^{\prime\prime}(t)+\frac{K}{t}x^{\prime}(t)+\nabla\Phi(x(t))=0,$ where $K>3$ and $\Phi$\ is a smooth convex function defined on a Hilbert space $\mathcal{H}.$ Moreover, we improve their result on the rate of convergence of $\Phi(x(t))-\min\Phi.$
Existence, Global Nonexistence, And Asymptotic Behavior Of Solutions For The Cauchy Problem Of A Multidimensional Generalized Damped Boussinesq-Type Equation, Erhan Pi̇şki̇n, Necat Polat
Existence, Global Nonexistence, And Asymptotic Behavior Of Solutions For The Cauchy Problem Of A Multidimensional Generalized Damped Boussinesq-Type Equation, Erhan Pi̇şki̇n, Necat Polat
Turkish Journal of Mathematics
We consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.