- Middle East Technical University, Mathematics, Faculty Memberadd
- He is a professor of mathematics with expertise on ordinary and functional differential equations, difference equatio... moreHe is a professor of mathematics with expertise on ordinary and functional differential equations, difference equations, impulsive systems, and dynamic equations on time scales. His work has been applied to nonlinear oscillation theory, boundary value problems, and mathematical modelling. He has published over 120 articles with more than 1300 citations. He also serves as an associate editor in several journals.edit
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Research Interests: Mathematics and Physics
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.... 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 ...
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We present Wong-type oscillation criteria for nonlinear impulsive differential equations having discontinuous solutions and involving both negative and positive coefficients. We use a technique that involves the use of a nonprincipal... more
We present Wong-type oscillation criteria for nonlinear impulsive differential equations having discontinuous solutions and involving both negative and positive coefficients. We use a technique that involves the use of a nonprincipal solution of the associated linear homogeneous equation. The existence of principal and nonpricipal solutions was recently obtained by the present authors in [J. Math. Anal. Appl. 503 (2021) 125311]. As special cases, we have superlinear and sublinear Emden-Fowler equations under impulse effects. It is shown that the oscillation behavior changes due to impulses, in particular impulses acting on the solution itself, not on its derivative. An example is also given to illustrate the importance of the results.
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Time scale approach allows one to treat the continuous, discrete, as well as more general systems simultaneously. In this paper we establish a Levinson type theorem and a Yakubovich type result on asymptotic equivalence of linear dynamic... more
Time scale approach allows one to treat the continuous, discrete, as well as more general systems simultaneously. In this paper we establish a Levinson type theorem and a Yakubovich type result on asymptotic equivalence of linear dynamic equations and linear and quasilinear dynamic equations, respectively.
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Abstract. A Langenhop-type inequality is given for dynamic equations on time scales. This result is further employed to obtain lower bounds for solutions of certain dynamic equations. As an application, usage of the derived Langenhop’s... more
Abstract. A Langenhop-type inequality is given for dynamic equations on time scales. This result is further employed to obtain lower bounds for solutions of certain dynamic equations. As an application, usage of the derived Langenhop’s inequality in determining the oscillatory behavior of a damped second order delay dynamic equation is illustrated. The results obtained are important in the qualitative sense. Key words. Langenhop inequality, time scale, lower bounds, oscillation AMS subject classications. 26D20, 34A40, 34K11 1. Introduction. There
We derive sufficient conditions for the oscillation of solutions second-order delay differential equation containing a sublinear neutral term. Our conditions differ from the earlier ones even in the special cases, linear or nonlinear, and... more
We derive sufficient conditions for the oscillation of solutions second-order delay differential equation containing a sublinear neutral term. Our conditions differ from the earlier ones even in the special cases, linear or nonlinear, and as illustrated with an example, we not only extend but also improve several results in the literature.
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Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler... more
Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type:x″(t)+p(t)|x(τ(t))|α-1x(τ(t))=0,t≠θk;Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0;Δx(t)|t=θk=0, (0
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The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform... more
The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.
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By means of certain functional relations, the equivalence of impulsive delay differential equations and impulsive differential equations is established. Based on some well known results for impulsive differential equations and for delay... more
By means of certain functional relations, the equivalence of impulsive delay differential equations and impulsive differential equations is established. Based on some well known results for impulsive differential equations and for delay differential equations, nontrivial consequences on existence and nonexistence of periodic solutions of impulsive delay differential equations are obtained. Key words: Impulse, Delay, Periodic solutions, Functional equivalence.
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View all references]. Therefore, the qualitative theory of partial difference equations has received considerable attention in the last decade, see 22. Agarwal, RP and Zhou, Y. 2000. Oscillation of partial difference equations with... more
View all references]. Therefore, the qualitative theory of partial difference equations has received considerable attention in the last decade, see 22. Agarwal, RP and Zhou, Y. 2000. Oscillation of partial difference equations with continuous variables. Math. Comput. Model. , 31: 17–29. [CrossRef], [Web of Science ®] View all references 11-14 View all references and the references cited therein. Impulsive differential equations appear as a natural description of observed evolution phenomena of several real-world problems [55. Bainov, DD and Simeonov, PS 1998. ...
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Page 1. Dynamical Systems and Differential Equations Joseph Páez Chávez Instituto de Ciencias Matemáticas, Escuela Superior Politécnica del Litoral, Km. 30.5 Vıa Perimetral, PO Box 09-01-5863 Guayaquil, Ecuador jpaez@espol.edu.ec August... more
Page 1. Dynamical Systems and Differential Equations Joseph Páez Chávez Instituto de Ciencias Matemáticas, Escuela Superior Politécnica del Litoral, Km. 30.5 Vıa Perimetral, PO Box 09-01-5863 Guayaquil, Ecuador jpaez@espol.edu.ec August 26, 2010 Abstract ...