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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
On Lyapunov-Type Inequalities For Five Different Types Of Higher Order Boundary Value Problems, Mustafa Fahri̇ Aktaş, Bariş Berkay Erçikti
On Lyapunov-Type Inequalities For Five Different Types Of Higher Order Boundary Value Problems, Mustafa Fahri̇ Aktaş, Bariş Berkay Erçikti
Turkish Journal of Mathematics
In this paper, we establish the uniqueness and existence of the classical solution to higher-order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher order boundary value problems. Our study is based on Green’s functions corresponding to the five different types of two-point boundary value problems. In addition, some applications of the obtained inequalities are given.
Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir
Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir
Turkish Journal of Mathematics
In this article we investigate the IVPs for 1-dimensional and 2-dimensional Boussinesq equations. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions for the considered IVPs. The arguments are based upon recent theoretical results.
Boundary Value Problems For A Second-Order $(P,Q) $-Difference Equation With Integral Conditions, İlker Gençtürk
Boundary Value Problems For A Second-Order $(P,Q) $-Difference Equation With Integral Conditions, İlker Gençtürk
Turkish Journal of Mathematics
Our purpose in this paper is to obtain some new existence results of solutions for a boundary value problem for a $ (p,q) $-difference equations with integral conditions, by using fixed point theorems. Examples illustrating the main results are also presented.
On The Existence For Parametric Boundary Value Problems Of A Coupled System Of Nonlinear Fractional Hybrid Differential Equations, Yige Zhao, Yibing Sun
On The Existence For Parametric Boundary Value Problems Of A Coupled System Of Nonlinear Fractional Hybrid Differential Equations, Yige Zhao, Yibing Sun
Turkish Journal of Mathematics
In this paper, we consider the existence and uniqueness for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations. By the fixed point theorem in Banach algebra, an existence theorem for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is given. Further, a uniqueness result for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is proved due to Banach's contraction principle. Further, we give three examples to verify the main results.
Inverse Coefficient Identification Problem For A Hyperbolic Equation With Nonlocal Integral Condition, Azizbayov Elvin
Inverse Coefficient Identification Problem For A Hyperbolic Equation With Nonlocal Integral Condition, Azizbayov Elvin
Turkish Journal of Mathematics
This paper is concerned with an inverse coefficient identification problem for a hyperbolic equation in a rectangular domain with a nonlocal integral condition. We introduce the definition of the classical solution, and then the considered problem is reduced to an auxiliary equivalent problem. Further, the existence and uniqueness of the solution of the equivalent problem are proved using a contraction mapping principle. Finally, using equivalency, the unique existence of a classical solution is proved.
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the Leray-Schauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).
Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal
Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal
Turkish Journal of Mathematics
In this paper, by using Parseval's formula and Schauder's fixed point theorem, we prove the existence and uniqueness of rotating periodic integrable solution of the second-order system $x''+f(t,x)=0$ with $x(t+T)=Qx(t)$ and $\int_{(k-1)T}^{kT}x(s)ds=0$, $k\in Z^+$ for any orthogonal matrix $Q$ when the nonlinearity $f$ satisfies nonresonance condition.
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System, Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Ulam-Hyers Stability Results For A Novel Nonlinear Nabla Caputo Fractional Variable-Order Difference System, Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Turkish Journal of Mathematics
This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variable-order and fixed initial valuable. By applying Krasnoselskii's fixed point theorem, we give some sufficient conditions to guarantee the existence results for the considered fractional discrete equations. In addition, we further consider the Ulam-Hyers stability by means of generalized Gronwall inequality. At last, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.
Existence Of Unique Solution To Switchedfractional Differential Equations With $P$-Laplacian Operator, Xiufeng Guo
Existence Of Unique Solution To Switchedfractional Differential Equations With $P$-Laplacian Operator, Xiufeng Guo
Turkish Journal of Mathematics
In this paper, we study a class of nonlinear switched systems of fractional order with $p$-Laplacian operator. By applying a fixed point theorem for a concave operator on a cone, we obtain the existence and uniqueness of a positive solution for an integral boundary value problem with switched nonlinearity under some suitable assumptions. An illustrative example is included to show that the obtained results are effective.
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.