Paper's Title:

Improved Oscillation Criteria of Second-Order Advanced Non-canonical Difference Equation

Author(s):

G. E. Chatzarakis¹, N. Indrajith², S. L. Panetsos¹, E. Thandapani³

¹Department of Electrical and Electronic Engineering Educators
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail: gea.xatz@aspete.gr, geaxatz@otenet.gr
spanetsos@aspete.gr

²Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

³Ramanujan Institute for Advanced Study in Mathematics,
University of Madras Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

Abstract:

Employing monotonic properties of nonoscillatory solutions, we derive some new oscillation criteria for the second-order advanced non-canonical difference equation

Our results extend and improve the earlier ones. The outcome is illustrated via some particular difference equations.

Paper's Title:

Oscillatory Behavior of Second-Order Non-Canonical Retarded Difference Equations

Author(s):

G.E. Chatzarakis¹, N. Indrajith², E. Thandapani³ and K.S. Vidhyaa⁴

¹Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail:  gea.xatz@aspete.gr, geaxatz@otenet.gr
 

²Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

³Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

⁴Department of Mathematics,
SRM Easwari Engineering College,
Chennai-600089,
India.
E-mail: vidyacertain@gmail.com

Abstract:

Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the second-order non-canonical difference equation with retarded argument

Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.

Paper's Title:

Oscillations of First Order Linear Delay Difference Equations

Author(s):

G. E. Chatzarakis and I. P. Stavroulakis

Department of Mathematics, University of Ioannina,
451 10, Greece
ipstav@cc.uoi.gr

Abstract:

Consider the first order linear delay difference equation of the form   where  is a sequence of nonnegative real numbers, k is a positive integer and  denotes the forward difference operator  New oscillation criteria are established when the well-known oscillation conditions  and  are not satisfied. The results obtained essentially improve known results in the literature.

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