


Paper's Title:
On Oscillation of SecondOrder Delay Dynamic Equations on Time Scales
Author(s):
S. H. Saker
Department of Mathematics, Faculty of Science,
Mansoura University, Mansoura, 35516,
Egypt.
shsaker@mans.edu.eg
Abstract:
Some new oscillation criteria for secondorder linear delay dynamic equation on a time scale T are established. Our results improve the recent results for delay dynamic equations and in the special case when T=R, the results include the oscillation results established by Hille [1948, Trans. Amer. Math. Soc. 64 (1948), 234252] and Erbe [Canad. Math. Bull. 16 (1973), 4956.] for differential equations. When T=Z the results include and improve some oscillation criteria for difference equations. When T=hZ, h>0, T=q^{N} and T=N^{2}, i.e., for generalized second order delay difference equations our results are essentially new and can be applied on different types of time scales. An example is considered to illustrate the main results.
Paper's Title:
On the Biharmonic Equation with Nonlinear Boundary Integral Conditions
Author(s):
R. Hamdouche and H. Saker
L.M.A. Department of Mathematics, Faculty
of Sciences,
University of Badji Mokhtar,
P.O.Box 12. Annaba 23000,
Algeria.
Email: h_saker@yahoo.fr,
hmdch.rahma16@gmail.com
Abstract:
In the present work, we deal with the biharmonic problems in a bounded domain in the plane with the nonlinear boundary integral conditions. After applying the Boundary integral method, a system of nonlinear boundary integral equations is obtained. The result show that when the nonlinearity satisfies some conditions lead the existence and uniqueness of the solution.
Paper's Title:
Oscillatory Behavior of SecondOrder NonCanonical Retarded Difference Equations
Author(s):
G.E. Chatzarakis^{1}, N. Indrajith^{2}, E. Thandapani^{3} and K.S. Vidhyaa^{4}
^{1}Department
of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
Email: gea.xatz@aspete.gr,
geaxatz@otenet.gr
^{2}Department
of Mathematics,
Presidency College, Chennai  600 005,
India.
Email: indrajithna@gmail.com
^{3}Ramanujan
Institute for Advanced Study in Mathematics,
University of Madras,
Chennai  600 005,
India.
Email: ethandapani@yahoo.co.in
^{4}Department of
Mathematics,
SRM Easwari Engineering College,
Chennai600089,
India.
Email: vidyacertain@gmail.com
Abstract:
Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the secondorder noncanonical difference equation with retarded argument
Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.
Paper's Title:
Improved Oscillation Criteria of SecondOrder Advanced Noncanonical Difference Equation
Author(s):
G. E. Chatzarakis^{1}, N. Indrajith^{2}, S. L. Panetsos^{1}, E. Thandapani^{3}
^{1}Department
of Electrical and Electronic Engineering Educators
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
Email: gea.xatz@aspete.gr,
geaxatz@otenet.gr
spanetsos@aspete.gr
^{2}Department
of Mathematics,
Presidency College, Chennai  600 005,
India.
Email: indrajithna@gmail.com
^{3}Ramanujan
Institute for Advanced Study in Mathematics,
University of Madras Chennai  600 005,
India.
Email: ethandapani@yahoo.co.in
Abstract:
Employing monotonic properties of nonoscillatory solutions, we derive some new oscillation criteria for the secondorder advanced noncanonical difference equation
Our results extend and improve the earlier ones. The outcome is illustrated via some particular difference equations.
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