1. Asst.Prof.Dr. Jessada Tariboon
Oscillation of Impulsive Functional
Differential Equations
Department of Mathematics, Faculty of Applied Science
Asst.Prof.Dr. Jessada Tariboon
King Mongkut’s University of Technology North Bangkok
OBJECTIVE
In this research, we investigate the oscillation of a class of second-order impulsive differential equations of the form
By using the equivalence transformation and the associated Riccati techniques, some interesting results are obtained.
METHODOLOGY
METHODOLOGY
Lemma 2.1 If the second-order differential equation
is oscillatory, then Eq. (1.1) is oscillatory, where
Lemma 2.2 (Leighton type oscillation criteria) Assume that the functions and If
and
then
is oscillatory.
Theorem 2.3 Assume that
Where Then Eq. (1.1) is oscillatory.
If then and (1.1) becomes
Theorem 2.4 Eq. (2.2) is oscillatory if and only if
is oscillatory.
Corollary 2.5 Assume that
and
Then Eq. (2.2) is oscillatory.
RESULTS & DISCUSSION
Figure 1: Time history of x(t).
Acknowledgement
This research work is financially supported by the Office of the Higher Education Commission, and King Mongkut’s University of Technology North Bangkok (contract no. 2555A ).
Contact
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand