Abdullah Özbekler - Academia.edu (original) (raw)

Papers by Abdullah Özbekler

Springer eBooks, 2021

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Journal of Integral Equations and Applications, Aug 1, 2018

In this paper, we give new oscillation criteria for discrete Volterra equations having different ... more In this paper, we give new oscillation criteria for discrete Volterra equations having different nonlinearities such as super-linear and sub-linear cases. We also present some new sufficient conditions for oscillation under the effect of the oscillatory forcing term. 2010 AMS Mathematics subject classification. Primary 39A10, 39A21.

Filomat, 2017

In this paper, Sturmian comparison theory is developed for the pair of second order differential ... more In this paper, Sturmian comparison theory is developed for the pair of second order differential equations; first of which is the nonlinear differential equations of the form (m(t)Φ β (y)) + n i=1 q i (t)Φ α i (y) = 0 (1) and the second is the half-linear differential equations (k(t)Φ β (x)) + p(t)Φ β (x) = 0 (2) where Φ * (s) = |s| * −1 s and α 1 > • • • > α m > β > α m+1 > • • • > α n > 0. Under the assumption that the solution of Eq. (2) has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for Eq. (1) by employing the new nonlinear version of Picone's formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for Eq. (1). Examples are given to illustrate the relevance of the results.

Springer eBooks, 2021

ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differ... more ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in N−N-N−dimensional domains Omega\OmegaOmega. We also consider singular and degenerate elliptic problems with ApA_pAp coefficients involving the p−p-p−Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the p−p-p−Laplacian, and compare them with the usual ones in the literature.

Lyapunov Inequalities and Applications, 2021

Journal of Mathematical Sciences, 2017

It is observed that the oscillation behavior may be altered due to presence of the delay. The ext... more It is observed that the oscillation behavior may be altered due to presence of the delay. The extensions to Emden-Fowler-type delay differential equations are also discussed.

Lyapunov Inequalities and Applications, 2021

ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differ... more ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in N−N-N−dimensional domains Omega\OmegaOmega. We also consider singular and degenerate elliptic problems with ApA_pAp coefficients involving the p−p-p−Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the p−p-p−Laplacian, and compare them with the usual ones in the literature.

Electronic Journal of Differential Equations, Jun 29, 2023

We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equati... more We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to 0 or ∞. Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works.

Miskolc Mathematical Notes

By employing Green's function, we obtain new Lyapunov and Hartman-type inequalities for higher-or... more By employing Green's function, we obtain new Lyapunov and Hartman-type inequalities for higher-order discrete fractional boundary value problems. Reported results essentially generalize some theorems existing in the literature. As an application, we discuss the corresponding eigenvalue problems.

atlas-conferences.com

Atlas home || Conferences | Abstracts | about Atlas 11'th Workshop on Dynamical Systems and ... more Atlas home || Conferences | Abstracts | about Atlas 11'th Workshop on Dynamical Systems and Applications June 26-28, 2012 Cankaya University Ankara, TURKEY. Organizers Billur Kaymakcalan, Agacik Zafer. Conference Homepage. Abstracts. Niyaz İSMAGİLOV On Pathwise Optimality for Controlled Diffusion type Processes Yeter ŞAHİNER On Oscillation of Elliptic Inequalities Murat ŞAT Inverse Problem For Interior Spectral Data of The Hydrogen ...

Applied Mathematics and Computation, Apr 1, 2010

We introduce the concept of principal and nonprincipal solutions for second order differential eq... more We introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results.

STURM COMPARISON THEORY FOR IMPULSIVE DIFFERENTIAL EQUATIONS ÖZBEKLER, Abdullah Ph.D., Department... more STURM COMPARISON THEORY FOR IMPULSIVE DIFFERENTIAL EQUATIONS ÖZBEKLER, Abdullah Ph.D., Department of Mathematics Supervisor: Prof. Dr. Ağacık ZAFER December 2005, 72 pages In this thesis, we investigate Sturmian comparison theory and oscillation for second order impulsive differential equations with fixed moments of impulse actions. It is shown that impulse actions may greatly alter the oscillation behavior of solutions. In chapter two, besides Sturmian type comparison results, we give Leightonian type comparison theorems and obtain Wirtinger type inequalities for linear, half-linear and non-selfadjoint equations. We present analogous results for forced super linear and super half-linear equations with damping. In chapter three, we derive sufficient conditions for oscillation of nonlinear equations. Integral averaging, function averaging techniques as well as interval criteria for oscillation are discussed. Oscillation criteria for solutions of impulsive Hill’s equation with damping...

Mathematical Methods in the Applied Sciences, 2018

In this paper, we give new oscillation criteria for forced sublinear impulsive differential equat... more In this paper, we give new oscillation criteria for forced sublinear impulsive differential equations of the form (r(t)x ′) ′ + q(t)|x| −1 x = (t), t ≠ i ; Δr(t)x ′ + q i |x| −1 x = i , t = i , where ∈ (0, 1), under the assumption that associated homogenous linear equation (r(t)z ′) ′ + q(t)z = 0, t ≠ i ; Δr(t)z ′ + q i z = 0, t = i is nonoscillatory.

Mathematics, 2019

In studying the Riccati transformation technique, some mathematical inequalities and comparison r... more In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.

Mathematical Methods in the Applied Sciences, 2015

In the paper, we give new oscillation criteria for Volterra integral equations having different n... more In the paper, we give new oscillation criteria for Volterra integral equations having different nonlinearities such as superlinearity and sublinearity. We also present some new sufficient conditions for oscillation under the effect of oscillatory forcing term.

Springer eBooks, 2021

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Journal of Integral Equations and Applications, Aug 1, 2018

In this paper, we give new oscillation criteria for discrete Volterra equations having different ... more In this paper, we give new oscillation criteria for discrete Volterra equations having different nonlinearities such as super-linear and sub-linear cases. We also present some new sufficient conditions for oscillation under the effect of the oscillatory forcing term. 2010 AMS Mathematics subject classification. Primary 39A10, 39A21.

Filomat, 2017

In this paper, Sturmian comparison theory is developed for the pair of second order differential ... more In this paper, Sturmian comparison theory is developed for the pair of second order differential equations; first of which is the nonlinear differential equations of the form (m(t)Φ β (y)) + n i=1 q i (t)Φ α i (y) = 0 (1) and the second is the half-linear differential equations (k(t)Φ β (x)) + p(t)Φ β (x) = 0 (2) where Φ * (s) = |s| * −1 s and α 1 > • • • > α m > β > α m+1 > • • • > α n > 0. Under the assumption that the solution of Eq. (2) has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for Eq. (1) by employing the new nonlinear version of Picone's formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for Eq. (1). Examples are given to illustrate the relevance of the results.

Springer eBooks, 2021

ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differ... more ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in N−N-N−dimensional domains Omega\OmegaOmega. We also consider singular and degenerate elliptic problems with ApA_pAp coefficients involving the p−p-p−Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the p−p-p−Laplacian, and compare them with the usual ones in the literature.

Lyapunov Inequalities and Applications, 2021

Journal of Mathematical Sciences, 2017

It is observed that the oscillation behavior may be altered due to presence of the delay. The ext... more It is observed that the oscillation behavior may be altered due to presence of the delay. The extensions to Emden-Fowler-type delay differential equations are also discussed.

Lyapunov Inequalities and Applications, 2021

ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differ... more ABSTRACT In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in N−N-N−dimensional domains Omega\OmegaOmega. We also consider singular and degenerate elliptic problems with ApA_pAp coefficients involving the p−p-p−Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the p−p-p−Laplacian, and compare them with the usual ones in the literature.

Electronic Journal of Differential Equations, Jun 29, 2023

We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equati... more We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to 0 or ∞. Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works.

Miskolc Mathematical Notes

By employing Green's function, we obtain new Lyapunov and Hartman-type inequalities for higher-or... more By employing Green's function, we obtain new Lyapunov and Hartman-type inequalities for higher-order discrete fractional boundary value problems. Reported results essentially generalize some theorems existing in the literature. As an application, we discuss the corresponding eigenvalue problems.

atlas-conferences.com

Atlas home || Conferences | Abstracts | about Atlas 11'th Workshop on Dynamical Systems and ... more Atlas home || Conferences | Abstracts | about Atlas 11'th Workshop on Dynamical Systems and Applications June 26-28, 2012 Cankaya University Ankara, TURKEY. Organizers Billur Kaymakcalan, Agacik Zafer. Conference Homepage. Abstracts. Niyaz İSMAGİLOV On Pathwise Optimality for Controlled Diffusion type Processes Yeter ŞAHİNER On Oscillation of Elliptic Inequalities Murat ŞAT Inverse Problem For Interior Spectral Data of The Hydrogen ...

Applied Mathematics and Computation, Apr 1, 2010

We introduce the concept of principal and nonprincipal solutions for second order differential eq... more We introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results.

STURM COMPARISON THEORY FOR IMPULSIVE DIFFERENTIAL EQUATIONS ÖZBEKLER, Abdullah Ph.D., Department... more STURM COMPARISON THEORY FOR IMPULSIVE DIFFERENTIAL EQUATIONS ÖZBEKLER, Abdullah Ph.D., Department of Mathematics Supervisor: Prof. Dr. Ağacık ZAFER December 2005, 72 pages In this thesis, we investigate Sturmian comparison theory and oscillation for second order impulsive differential equations with fixed moments of impulse actions. It is shown that impulse actions may greatly alter the oscillation behavior of solutions. In chapter two, besides Sturmian type comparison results, we give Leightonian type comparison theorems and obtain Wirtinger type inequalities for linear, half-linear and non-selfadjoint equations. We present analogous results for forced super linear and super half-linear equations with damping. In chapter three, we derive sufficient conditions for oscillation of nonlinear equations. Integral averaging, function averaging techniques as well as interval criteria for oscillation are discussed. Oscillation criteria for solutions of impulsive Hill’s equation with damping...

Mathematical Methods in the Applied Sciences, 2018

In this paper, we give new oscillation criteria for forced sublinear impulsive differential equat... more In this paper, we give new oscillation criteria for forced sublinear impulsive differential equations of the form (r(t)x ′) ′ + q(t)|x| −1 x = (t), t ≠ i ; Δr(t)x ′ + q i |x| −1 x = i , t = i , where ∈ (0, 1), under the assumption that associated homogenous linear equation (r(t)z ′) ′ + q(t)z = 0, t ≠ i ; Δr(t)z ′ + q i z = 0, t = i is nonoscillatory.

Mathematics, 2019

In studying the Riccati transformation technique, some mathematical inequalities and comparison r... more In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.

Mathematical Methods in the Applied Sciences, 2015

In the paper, we give new oscillation criteria for Volterra integral equations having different n... more In the paper, we give new oscillation criteria for Volterra integral equations having different nonlinearities such as superlinearity and sublinearity. We also present some new sufficient conditions for oscillation under the effect of oscillatory forcing term.