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Articles 1 - 17 of 17
Full-Text Articles in Physical Sciences and Mathematics
On Positive Periodic Solutions To Third-Order Integro-Differential Equations With Distributed Delays, Mimia Benhadri, Tomas Caraballo
On Positive Periodic Solutions To Third-Order Integro-Differential Equations With Distributed Delays, Mimia Benhadri, Tomas Caraballo
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integro-differential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results.
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad
Turkish Journal of Mathematics
In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales $$ \begin{aligned} &\mathcal{T}_α^{\Delta}\big[\mathcal{T}_β^{\Delta}\big(\vartheta_\mathtt{n}(t)\big)\big]=\varphi(t)\mathtt{f}_\mathtt{n}\left(\vartheta_{\mathtt{n}+1}(t)\right),~t\in(0,1)_\mathbb{T},~1
Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan
Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan
Turkish Journal of Mathematics
In this paper, by using fixed point theorem we establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of certain homogeneous Fredholm Integral equation of the second kind $$ \phi(x) = \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ and the nonhomogeneous equation $$ \phi(x) = x + \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ for all $x \in [0,1]$ and $0
On Bounded Solutions Of A Second-Order Iterative Boundary Value Problem, Safa Chouaf, Ahleme Bouakkaz, Rabah Khemis
On Bounded Solutions Of A Second-Order Iterative Boundary Value Problem, Safa Chouaf, Ahleme Bouakkaz, Rabah Khemis
Turkish Journal of Mathematics
In this article, we investigate a second-order iterative differential equation with boundary conditions. The use of the principle of contraction mappings and the Schauder's fixed point theorem allows us to prove some existence and uniqueness results. Finally, an example is given to check the validity of our findings, which are new, and complete some published manuscripts to some degree.
A Discussion On The Existence And Uniqueness Analysis For The Coupled Two-Term Fractional Differential Equations, Sachin Kumar Verma, Ramesh Kumar Vats, Avadhesh Kumar, Velusamy Vijayakumar, Anurag Shukla
A Discussion On The Existence And Uniqueness Analysis For The Coupled Two-Term Fractional Differential Equations, Sachin Kumar Verma, Ramesh Kumar Vats, Avadhesh Kumar, Velusamy Vijayakumar, Anurag Shukla
Turkish Journal of Mathematics
This paper mainly concentrates on the study of a new boundary value problem of coupled nonlinear two-term fractional differential system. We make use of the theories on fractional calculus and fixed point approach to derive the existence and uniqueness results of the considered two-term fractional systems. To confirm the application of the stated outcomes, two examples are provided.
A Fixed Point Theorem Using Condensing Operators And Its Applications To Erdelyi--Kober Bivariate Fractional Integral Equations, Anupam Das, Mohsen Rabbani, Bipan Hazarika, Sumati Kumari Panda
A Fixed Point Theorem Using Condensing Operators And Its Applications To Erdelyi--Kober Bivariate Fractional Integral Equations, Anupam Das, Mohsen Rabbani, Bipan Hazarika, Sumati Kumari Panda
Turkish Journal of Mathematics
The primary aim of this article is to discuss and prove fixed point results using the operator type condensing map, and to obtain the existence of solution of Erdelyi-Kober bivariate fractional integral equation in a Banach space. An instance is given to explain the results obtained, and we construct an iterative algorithm by sinc interpolation to find an approximate solution of the problem with acceptable accuracy.
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Turkish Journal of Mathematics
In this paper, we consider a class of second order differential equations with iterative source term. The main results are obtained by virtue of a Krasnoselskii fixed point theorem and some useful properties of a Green's function which allows us to prove the existence of positive periodic solutions. Finally, an example is included to illustrate the correctness of our results.
Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir
Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir
Turkish Journal of Mathematics
This research article deals with novel two species of initial value problems, one of them, the fractional neutral functional integrodifferential equations, and the other one, the coupled system of fractional neutral functional integrodifferential equations, with finite delay and involving a $\psi$-Caputo fractional operator. The existence and uniqueness results are studied through Banach's contraction principle and Krasnoselskii's fixed point theorem. We also establish two various kinds of Ulam stability results for the proposed problems. Further, two pertinent examples are presented to demonstrate the reported results.
Solutions To Nonlinear Second-Order Three-Point Boundary Value Problems Of Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Solutions To Nonlinear Second-Order Three-Point Boundary Value Problems Of Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for $p$-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional $ p $-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; …
On Positive Periodic Solutions Of Second-Order Semipositonedifferential Equations, Fanglei Wang, Nannan Yang
On Positive Periodic Solutions Of Second-Order Semipositonedifferential Equations, Fanglei Wang, Nannan Yang
Turkish Journal of Mathematics
Using the Krasnosel'skii's fixed point theorem, we establish the existence and multiplicity of positive $\mathrm{T}$-periodic solutions of second-order semipositone system $ \left \{\begin{array}{lcr} x''(t)+a(t)x(t)=\lambda f(t,x(t)),\\ x(0)=x(\mathrm{T}),x'(0)=x'(\mathrm{T}), \end{array}\right. $ where $x=(x_1,x_2,\cdots,x_n)$, $f(t,x)=(f_1(t,x),f_2(t,x),\cdots,f_n(t,x))$ is bounded below.
On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An
On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An
Turkish Journal of Mathematics
In this paper,we obtain some new existence, uniqueness, and multiplicity results of radial solutions of an elliptic system coupled by Monge-Ampére equations using the fixed point theorem.
Analysis Of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition, Tuğba Akman Yildiz, Neda Khodabakhshi, Dumitru Baleanu
Analysis Of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition, Tuğba Akman Yildiz, Neda Khodabakhshi, Dumitru Baleanu
Turkish Journal of Mathematics
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.
Solvability Of Boundary Value Problems For Coupled Impulsive Differential Equations With One-Dimensional P-Laplacians, Yuji Liu
Turkish Journal of Mathematics
This paper is concerned with a boundary value problem of impulsive differential systems on the whole line with one-dimensional p-Laplacians. By constructing a weighted Banach space and defining a nonlinear operator, together with Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established (Theorems 3.1-3.3). Two examples are given to illustrate the main results.
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we study the existence of positive solutions of a nonlinear $ m $-point $p$-Laplacian dynamic equation $$(\phi_p(x^\Delta(t)))^\nabla+w(t)f(t,x(t),x^\Delta(t))=0,\hspace{2cm} t_1< t 1.$ Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term $f$ is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.
Solutions For 2n^{Th} Order Lidstone Bvp On Time Scales, Erbi̇l Çeti̇n, S. Gülşan Topal
Solutions For 2n^{Th} Order Lidstone Bvp On Time Scales, Erbi̇l Çeti̇n, S. Gülşan Topal
Turkish Journal of Mathematics
In this paper, we prove the existence of solutions for nonlinear Lidstone boundary value problems by using the monotone method on time scale and also we show the existence of at least one positive solution if f is either superlinear or sublinear by the fixed point theorem in a Banach space.
Extension Of Caristi-Kirk's Theorem, M. O. Diallo, M. Oudadess
Extension Of Caristi-Kirk's Theorem, M. O. Diallo, M. Oudadess
Turkish Journal of Mathematics
We give some extensions and/or improvements, to uniform spaces and to multi-valued mappings, of Caristi-Kirk's theorem.