Abdulkadir Dogan - Academia.edu (original) (raw)

Papers by Abdulkadir Dogan

Research paper thumbnail of Multiple positive solutions of nonlinear <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span>-point dynamic equations for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span></span></span></span>-Laplacian on time scales

TURKISH JOURNAL OF MATHEMATICS, 2016

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Research paper thumbnail of Impact of peer-to-peer communication on real-time performance of file replication algorithms

2008 23rd International Symposium on Computer and Information Sciences, 2008

Abstract A variety of file replication algorithms are proposed for Data Grids in the literature. ... more Abstract A variety of file replication algorithms are proposed for Data Grids in the literature. Most of these algorithms ignore real-time Grid applications which are emerging in many disciplines of science and engineering today. Thus, it is important to study and improve ...

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Research paper thumbnail of Eigenvalue Problems for Singular Multi-Point Dynamic Equations on Time Scales

In this article, we study a singular multi-point dynamic eigenvalue problem on time scales. We fi... more In this article, we study a singular multi-point dynamic eigenvalue problem on time scales. We find existence of positive solutions by constructing the Green's function and studying its positivity eigenvalue intervals. Two examples are given to illustrate our results.

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Research paper thumbnail of Solutions to nonlinear second-order three-point boundary value problems of dynamic equations on time scales

TURKISH JOURNAL OF MATHEMATICS, 2019

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Research paper thumbnail of POSITIVE SOLUTIONS OF THE p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES WITH SIGN CHANGING NONLINEARITY

This article concerns the existence of positive solutions for pLaplacian boundary value problem o... more This article concerns the existence of positive solutions for pLaplacian boundary value problem on time scales. By applying fixed point index we obtain the existence of solutions. Emphasis is put on the fact that the nonlinear term is allowed to change sign. An example illustrates our results.

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Research paper thumbnail of Existence of Countably Many Positive Solutions for Nonlinear Boundary Value Problems on Time Scales

Abstract: In this paper, we consider the existence of countably many positive solutions for nonli... more Abstract: In this paper, we consider the existence of countably many positive solutions for nonlinear singular boundary value problem on time scales. By using the fixed-point index theory and a new fixed-point theorem in cones, the sufficient conditions for the existence of countably many positive solutions are established.

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Research paper thumbnail of On the existence of positive solutions for the second-order boundary value problem

Applied Mathematics Letters

This paper is concerned with the existence of positive solutions to a second order boundary value... more This paper is concerned with the existence of positive solutions to a second order boundary value problem. By imposing growth conditions on and using a generalization of the Leggett–Williams fixed point theorem, we prove the existence of at least three symmetric positive solutions.

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Research paper thumbnail of TRIPLE POSITIVE SOLUTIONS FOR m-POINT BOUNDARY-VALUE PROBLEMS OF DYNAMIC EQUATIONS ON TIME SCALES WITH p-LAPLACIAN

In this article we study the existence of positive solutions for mpoint dynamic equation on time ... more In this article we study the existence of positive solutions for mpoint dynamic equation on time scales with p-Laplacian. We prove that the boundary-value problem has at least three positive solutions by applying the five functionals fixed-point theorem. An example demonstrates the main results.

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Research paper thumbnail of Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

Acta et Commentationes Universitatis Tartuensis de Mathematica

In this paper, the authors examine the existence of positive solutions to a third-order boundary ... more In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results.

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Research paper thumbnail of Existence of Countably Many Positive Solutions for Nonlinear Boundary Value Problems on Time Scales

Applied Mathematics & Information Sciences

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Research paper thumbnail of Eigenvalue problems for nonlinear third-orderm-pointp-Laplacian dynamic equations on time scales

Mathematical Methods in the Applied Sciences

ABSTRACT This work deals with the existence and uniqueness of a nontrivial solution for the third... more ABSTRACT This work deals with the existence and uniqueness of a nontrivial solution for the third-order p-Laplacian m-point eigenvalue problems on time scales. We find several sufficient conditions of the existence and uniqueness of nontrivial solution of eigenvalue problems when λ is in some interval. The proofs are based on the nonlinear alternative of Leray–Schauder. To illustrate the results, some examples are included. Copyright © 2014 John Wiley &amp; Sons, Ltd.

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Research paper thumbnail of On the existence of positive solutions of the p -Laplacian dynamic equations on time scales

Mathematical Methods in the Applied Sciences, 2017

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Research paper thumbnail of Higher order singular multipoint boundary value problems on time scales

We study classes of higher-order singular boundary-value problems on a time scale mathbbT\mathbb{T}mathbbT wi... more We study classes of higher-order singular boundary-value problems on a time scale mathbbT\mathbb{T}mathbbT with a positive parameter λ in the differential equations. A homeomorphism and homomorphism ø are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter λ is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.

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Research paper thumbnail of RLW equation using linear finite elements within Galerkin�s method

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Research paper thumbnail of A Petrov-Galerkin finite element scheme for Burgers’ equation

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING

Burgers’ equation is solved by a Petrov-Galerkin method using quadratic B-spline spatial finite e... more Burgers’ equation is solved by a Petrov-Galerkin method using quadratic B-spline spatial finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank-Nicolson approach involving a product approximation. Standard problems are solved to assess the properties of the algorithm.

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Research paper thumbnail of B-Spline Collocation Methods For Numerical Solutions Of The Rlw Equation

International Journal of Computer Mathematics, 2003

The numerical solution of the RLW equation is obtained by using a splitting up technique and both... more The numerical solution of the RLW equation is obtained by using a splitting up technique and both quadratic and cubic B-splines. Both quadratic and cubic B-spline collocation methods are applied to the resulting equation. Solutions without splitting the RLW ...

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Research paper thumbnail of Galerkin method for the numerical solution of the RLW equation using quadratic B-splines

International Journal of Computer Mathematics, 2004

A numerical solution of the Regularised Long Wave (RLW) Equation is obtained using space-splittin... more A numerical solution of the Regularised Long Wave (RLW) Equation is obtained using space-splitting technique and quadratic B-spline Galerkin finite element method. Solitary wave motion, interaction of two solitary waves and wave generation are studied using the proposed method. Comparisons are made with analytical solutions and with some spline finite element method calculations at selected times. Accuracy and efficiency are discussed by computing the numerical conserved laws and L2, L∞ norms.

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Research paper thumbnail of A least-squares finite element scheme for the RLW equation

Communications in Numerical Methods in Engineering, 1996

ABSTRACT The RLW equation is solved by a least-squares technique using linear space-time finite e... more ABSTRACT The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (≤ 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin&#39;s method. The development of an undular bore is modelled.

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Research paper thumbnail of Higher order semipositone multi-point boundary value problems on time scales

Computers & Mathematics with Applications, 2010

The authors obtain some existence criteria for positive solutions of a higher order semipositone ... more The authors obtain some existence criteria for positive solutions of a higher order semipositone multi-point boundary value problem on a time scale. Applications to some special problems are also discussed. This work extends and complements many results in the literature on this topic.

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Research paper thumbnail of Application of Galerkin's method to equal width wave equation

Applied Mathematics and Computation, 2005

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Research paper thumbnail of Multiple positive solutions of nonlinear <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span>-point dynamic equations for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span></span></span></span>-Laplacian on time scales

TURKISH JOURNAL OF MATHEMATICS, 2016

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Research paper thumbnail of Impact of peer-to-peer communication on real-time performance of file replication algorithms

2008 23rd International Symposium on Computer and Information Sciences, 2008

Abstract A variety of file replication algorithms are proposed for Data Grids in the literature. ... more Abstract A variety of file replication algorithms are proposed for Data Grids in the literature. Most of these algorithms ignore real-time Grid applications which are emerging in many disciplines of science and engineering today. Thus, it is important to study and improve ...

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Research paper thumbnail of Eigenvalue Problems for Singular Multi-Point Dynamic Equations on Time Scales

In this article, we study a singular multi-point dynamic eigenvalue problem on time scales. We fi... more In this article, we study a singular multi-point dynamic eigenvalue problem on time scales. We find existence of positive solutions by constructing the Green's function and studying its positivity eigenvalue intervals. Two examples are given to illustrate our results.

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Research paper thumbnail of Solutions to nonlinear second-order three-point boundary value problems of dynamic equations on time scales

TURKISH JOURNAL OF MATHEMATICS, 2019

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Research paper thumbnail of POSITIVE SOLUTIONS OF THE p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES WITH SIGN CHANGING NONLINEARITY

This article concerns the existence of positive solutions for pLaplacian boundary value problem o... more This article concerns the existence of positive solutions for pLaplacian boundary value problem on time scales. By applying fixed point index we obtain the existence of solutions. Emphasis is put on the fact that the nonlinear term is allowed to change sign. An example illustrates our results.

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Research paper thumbnail of Existence of Countably Many Positive Solutions for Nonlinear Boundary Value Problems on Time Scales

Abstract: In this paper, we consider the existence of countably many positive solutions for nonli... more Abstract: In this paper, we consider the existence of countably many positive solutions for nonlinear singular boundary value problem on time scales. By using the fixed-point index theory and a new fixed-point theorem in cones, the sufficient conditions for the existence of countably many positive solutions are established.

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Research paper thumbnail of On the existence of positive solutions for the second-order boundary value problem

Applied Mathematics Letters

This paper is concerned with the existence of positive solutions to a second order boundary value... more This paper is concerned with the existence of positive solutions to a second order boundary value problem. By imposing growth conditions on and using a generalization of the Leggett–Williams fixed point theorem, we prove the existence of at least three symmetric positive solutions.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of TRIPLE POSITIVE SOLUTIONS FOR m-POINT BOUNDARY-VALUE PROBLEMS OF DYNAMIC EQUATIONS ON TIME SCALES WITH p-LAPLACIAN

In this article we study the existence of positive solutions for mpoint dynamic equation on time ... more In this article we study the existence of positive solutions for mpoint dynamic equation on time scales with p-Laplacian. We prove that the boundary-value problem has at least three positive solutions by applying the five functionals fixed-point theorem. An example demonstrates the main results.

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Research paper thumbnail of Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

Acta et Commentationes Universitatis Tartuensis de Mathematica

In this paper, the authors examine the existence of positive solutions to a third-order boundary ... more In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results.

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Research paper thumbnail of Existence of Countably Many Positive Solutions for Nonlinear Boundary Value Problems on Time Scales

Applied Mathematics & Information Sciences

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Research paper thumbnail of Eigenvalue problems for nonlinear third-orderm-pointp-Laplacian dynamic equations on time scales

Mathematical Methods in the Applied Sciences

ABSTRACT This work deals with the existence and uniqueness of a nontrivial solution for the third... more ABSTRACT This work deals with the existence and uniqueness of a nontrivial solution for the third-order p-Laplacian m-point eigenvalue problems on time scales. We find several sufficient conditions of the existence and uniqueness of nontrivial solution of eigenvalue problems when λ is in some interval. The proofs are based on the nonlinear alternative of Leray–Schauder. To illustrate the results, some examples are included. Copyright © 2014 John Wiley &amp; Sons, Ltd.

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Research paper thumbnail of On the existence of positive solutions of the p -Laplacian dynamic equations on time scales

Mathematical Methods in the Applied Sciences, 2017

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Research paper thumbnail of Higher order singular multipoint boundary value problems on time scales

We study classes of higher-order singular boundary-value problems on a time scale mathbbT\mathbb{T}mathbbT wi... more We study classes of higher-order singular boundary-value problems on a time scale mathbbT\mathbb{T}mathbbT with a positive parameter λ in the differential equations. A homeomorphism and homomorphism ø are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter λ is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of RLW equation using linear finite elements within Galerkin�s method

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Petrov-Galerkin finite element scheme for Burgers’ equation

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING

Burgers’ equation is solved by a Petrov-Galerkin method using quadratic B-spline spatial finite e... more Burgers’ equation is solved by a Petrov-Galerkin method using quadratic B-spline spatial finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank-Nicolson approach involving a product approximation. Standard problems are solved to assess the properties of the algorithm.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of B-Spline Collocation Methods For Numerical Solutions Of The Rlw Equation

International Journal of Computer Mathematics, 2003

The numerical solution of the RLW equation is obtained by using a splitting up technique and both... more The numerical solution of the RLW equation is obtained by using a splitting up technique and both quadratic and cubic B-splines. Both quadratic and cubic B-spline collocation methods are applied to the resulting equation. Solutions without splitting the RLW ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Galerkin method for the numerical solution of the RLW equation using quadratic B-splines

International Journal of Computer Mathematics, 2004

A numerical solution of the Regularised Long Wave (RLW) Equation is obtained using space-splittin... more A numerical solution of the Regularised Long Wave (RLW) Equation is obtained using space-splitting technique and quadratic B-spline Galerkin finite element method. Solitary wave motion, interaction of two solitary waves and wave generation are studied using the proposed method. Comparisons are made with analytical solutions and with some spline finite element method calculations at selected times. Accuracy and efficiency are discussed by computing the numerical conserved laws and L2, L∞ norms.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A least-squares finite element scheme for the RLW equation

Communications in Numerical Methods in Engineering, 1996

ABSTRACT The RLW equation is solved by a least-squares technique using linear space-time finite e... more ABSTRACT The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (≤ 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin&#39;s method. The development of an undular bore is modelled.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Higher order semipositone multi-point boundary value problems on time scales

Computers & Mathematics with Applications, 2010

The authors obtain some existence criteria for positive solutions of a higher order semipositone ... more The authors obtain some existence criteria for positive solutions of a higher order semipositone multi-point boundary value problem on a time scale. Applications to some special problems are also discussed. This work extends and complements many results in the literature on this topic.

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Research paper thumbnail of Application of Galerkin's method to equal width wave equation

Applied Mathematics and Computation, 2005

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